25. (ye*" – 2y³) dx + (x e*' – 6xy² – 2y) dy = 0; when x = 0, y = 2. ANS. e* = 2xy³ + y² – 3.

Q: dy/dx if y=tan((1-2x)/(1+x)) dy/dx if y=x^4 ln(3x-1)

A: 1)    y=tan1-2x1+x2)    y=x4ln(3x-1) Hint:  Chain rule and then uv and u/v rule of differentiation

Q: Find the differential equation corresponding to y=a cos (logx) +b sin(logx) or y=A sin (logx)…

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Q: Show that given differential equation dy y cos x + sin y + 9 – 0 is Exact and dx sin x + x cos y + x…

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Q: Obtain the differential equation of the family of circles with center at point (h,k) and radius r.…

A: The equation of the circle having a center (h, K) and radius and radius r is given by:…

Q: Solve for the differential of y when y=sinzx, x=-, and dx=- 3 2

A: Pi/4

Q: (2y-1 + cos 3z) 분. 4x3 + 3y sin 3x = 0 (1)

A: We know that if - M(dy/dx)+N=0 Then M(dy/dx)= -N Therefore- dy/dx= -(N/M)

Q: 9. From the differential equation sinh 2x, sketch some of the family of curves. %3D dx

A: Given differential equation, dydx=sinh(2x)dydx=e2x-e-2x2∫dy=∫e2x-e-2x2dxy=e2x+e-2x4+C

Q: 3. find dy/dx of y= sinh 2x

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Q: 3. Show that the differential equation dx is homogenous. Zxy

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Q: Form the differential equation whose primitive is given by y= ex(a cos⁡x + b sin⁡x),  a, b, being…

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Q: 2 iii. sech x3 tanh( x3 S- -dx 1 X3

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Q: 28. Differentiate implicitly to find dy/dx if x + x/y = 7.

A: Given, x3+x/y=7 we can also write as yx3+x=7y,  or y=x7-x3 derivate both side w.r.t x…

Q: ind dy/dx if y=8x-3/24x^5

A:

Q: tanx dx = -In/secx|+C^O .BO In|secx|+CO In/cscx| +CO -In|cscx|+C°O .D

A: We need to evaluate the following integral I = ∫tanxdx

Q: show Itat the differential equation メり dy - -2-ye" dx xーとリ Xe 29 its exact and find its Folution

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Q: sinh (:) dz dy dx

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Q: From the differential equation by elimaniting arbitary constant  y=ax3+bx2

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Q: The differential equation ry" + 3y - 7y=seca is normal on any open interval not containing a = 0.…

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Q: Obtain the differential equation of the family of straight lines with slope and y-intercept equal.

A: Equation of straight line: y=mx+c Where, m = slope  c = y-intercept

Q: Which óf thé fóllówing directión fiéld will represent the differential equation y' = y + 1 Option 1…

A: Direction field: A graphical representation of solutions of a first order differential equation is…

Q: in differentials of functions, if x change by a small amount dx then, what will happen to y?

A: Let a function be y=fx then here y is the dependent variable and x is the independent variable. The…

Q: ① Solveing dy - - x dx = 。 ㅎ

A:

Q: - ((x3 + x)sech(In x)) = dx EX)-

A: To find  ddx(x3+x)(sech(ln x) We use product rule  d(uv)=udv+vdu Let  u=x3+x,     v=sech(ln…

Q: 5. 2x sinh+ 3y cosh2) dx -- 3x cosh dy = 0

A:

Q: The integrating factor of the linear differential equation – (tanx)y = x is_ - O sinx O log(cosa)…

A: Given dydx-tanxy=x

Q: 2 sinh 3x cosh 2y dx + 3 cosh 3x sinh 2y dy = 0

A: We know sinh xcosh x = tanh x ∫tanh ax dx = 1alncosh ax + C    (where C is constant of integration)

Q: From the differential equation by eliminationg the arbitary constant A,B from y=Ae/x+Be¬-7x +Be-7x

A: To form the differential equation by eliminating the arbitrary constant

Q: The integrating factor of the linear first order differential equation dy dx sin2x- y+tanx Oa None…

A: The standard formula for the linear differential equation is dydx+P(x)y=Q(x). Here, P(x), Q(x) are…

Q: 1. What is the integrating factor of the differential equation ydx – xdy = 0 using case 1?

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Q: Find the differential equation of family of circles tangent to the x-axis.

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Q: The differential equation corresponding to the family of curves y = Asin2x+ B cos 2x , where A and B…

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Q: al csc x y cotx

A: We have to find the intregating factor of given differential equation.

Q: 7. Find the differential dy of the function y = x (1-cos(x)). If the error in x is ", find the error…

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Q: i) S'(2x – 1)* dx (In x)2 j) fth dx 7 k) S (1-- -)dx (x2+1) 1) S(1+ tan² x) dx

A: I am attaching image so that you understand each and every step.

Q: Differentiate the following function.   y=ln(x+1)+ln7 dy/dx=?

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Q: 22. Find OY if y2 - 4xy + x² = 10. dx

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Q: Obtain the differential equation of all circles with center on line y = -x and passing through the…

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Q: find dy/dx of y=sin^2 4x+1/2 cos 8x

A: Given,         y=sin24x+12cos8x

Q: what is the differential coefficient of x.

A: To find differential coefficient of x we need to differentiate x with respect to x.

Q: a. Obtain the differential equation of the family of straight line with the algebraic sum of the…

A: Write general equation first of given conditions.

Q: 2. y"' + 4y' = sin x + 3 cos x

A:

Q: Evaluate the integrals

A: Given integral is:

Q: 4) S tanx dx cosxv1+secx 5) S(1- u)Vūdu

A: (4)  First we integrate this ∫tanxcosx1+secxdx

Q: Find dy/dx at (-4,1) if xy=(8y/(x+2)). dy/dx at (-4,1) =?

A: Derivative of any function determines the rate of change of a function. It is represented as dydx if…

Q: 12. Differentiate.   y=4/2−7x dy/dx=nothing   Enter your answer in the answer box.

A:

Q: Calculate the truncation error to solve the differential equation: Yi+1¬Yi = Xị → (*) Ax dy Instead…

A: Follow the following solutions to get the complete correct answer.