Find the following initial value problems. y²-1 ,y(0) = 0 dy dx х2-1 2.

Q: Find the exact solution y to the initial-value problem dy/dx= x y^(1/2), y(1) = 4.

A: It is exact solution to the initial value problem.

Q: Solve the initial value problem: dy = x(1+ y)²; dx y(0) = -3

A:

Q: Solve the initial value problem e*dx + (e*tany + 2secy)dy = 0, y(1) = 2

A: Given that exdx+extaby+2sec ydy=0, y(1)=2. This is of the form Mdx+Ndy=0. M=exMy=0 And…

Q: , solve the initial value problem.

A: dydx=yln y1+x2

Q: Solve the following initial-value problem: 3 dy +y2 = 1, y(0) = 4 dx

A: Given information: The differential equation is  y12dydx+y32=1 and the value y(0)=4

Q: Solve the initial value problem y dy/dx = sin 2x ; y(0)=2

A:

Q: Solve the following initial value problem, dy ry +x dx y(2) = 0,

A:

Q: slove the initial value problem: (dx/dt)-5x=cos(4t) with x(0)=5 find x(t)

A: The given initial value problem is: dxdt-5x=cos4t with x0=5. The given differential equation is a…

Q: dy .Solve the initial value problem +2y=e", y(0) =-1. dx

A:

Q: Solve the given initial-value problem: dy/dx =(y2 − 1)/(x2 − 1), y(2) = 2

A:

Q: Solve the initial value problem x2 dy/dx - 2xy=3y4, y(1)=1/2.

A: Solve the initial value problem x2 dy/dx - 2xy=3y4, y(1)=1/2.

Q: dy xe*- dx -In y Solve the initial value problem , y(0)=1. 6.2

A:

Q: Solve the initial value problem dy/dx=2/x+1, y(0)=2.

A:

Q: dy sin(t) + 1 dt

A:

Q: Solve the initial value problem dy/dx = sin(πx), y(2) = 2

A:

Q: Solve the initial value problems dy/dx = 1 + 1/x, y(1) = 3

A: The given initial value problem is dydx= 1 + 1x, y(1) = 3.

Q: dy 4. Solve the initial value problem : (1+x²). -= yx, y(1) = 2 dx

A: The given differential equation is 1+x2dydx=yx, y1=2.

Q: Solve the initial-value problems dy y(1) = 2 dx dy = cos t + 1, dt 2

A: To solve the given initial value problems

Q: If the function f (x) solves the initial value problem dy = (x +1)-1/2 – T · cos(T2) y(3) = 2 , %3D…

A: Given: dydx=x+1-12-π·cosπx Now separate the variables; dy=x+1-12-π·cosπxdx Now taking integral on…

Q: Find the particular solution for the initial value problem.

A:

Q: Solve the initial value problem. √y dx + (x-4)dy=0, y(5)= 36

A:

Q: Solve the following initial value problem. dy +x, x> 0; y(2) = 5 .3 dx

A: Given: dydx=1x3+x, x>0; y(2)=5

Q: Solve the initial value problem. dy + 9xy = 4x, y(0) = - 3 dx

A: This question is related to differential equations, we will solve it using given information.

Q: Find the solution of the initial value problem. dy dx 1+y y(0) =1 %3D

A:

Q: Find an implicit and an explicit solution of the given initial-value problem. dy y – 1 dx x? - 1'…

A:

Q: Solve the following initial value problem: 1 dy + 2ry? + (2a²y – cos(y)). 0, y(1) = . dx

A:

Q: find the initial value problem dy/dx = e^2, y(0)=2

A:

Q: Find the solution of the following initial value problem. dy = 3 x², y(0) = 9 dx y =

A:

Q: dy dx Vx x+1 Solve the initial-value problem y(1) =0.

A:

Q: Find the particular solution for initial value problem.

A:

Q: Solve the initial value problems dy/dx = (x + 1/x)2, y(1) = 1

A: The given differential equation is dydx=x+1x2.

Q: Solve the given initial value problem. dy + dx 1 3 xy-3, y(1) = 0 4x

A: Use substitution y^4=v and find integrating factor

Q: Solve the initial value problem. dy 1. dx y = xex, y(0) = e + 1

A:

Q: Solve the initial value problem: dy x(1+ y)²; y(0) = –3 dx

A:

Q: Solve the initial value problem.

A:

Q: Solve the initial value problem dy/dx + y = 2 sin x, y(0) = 1.

A: Given differential equation is Comparing it with  we get The integrating factor of the…

Q: Solve the following initial value problem for y: dy +e=2#, y(0) = 0 -2x COS dx

A:

Q: Solve the initial value problem: dy/dx= (1/(2sqrt(x)))+2 y(1)=3

A: Solving the initial value problem.

Q: Solve the given initial-value problem. dx y = 5y², x(9) = 1 dy

A:

Q: dy 6. Solve the initial value problem xy², y(0) = –1. dx %3D

A: Using seperation of variables.

Q: Solve the initial value problem. √y dx + (x-9)dy = 0, y(10) = 1

A: Sol:- ydx+x-9dy = 0 , y10=1It can be rewritten as :-ydx=-(x-9)dy

Q: Find the particular solution for each initial value problem.

A:

Q: Solve the initial value problem: (e + y) dx + (2 +x + ye") dy = 0, y(0) = 1

A: We have to solve the initial value problem…

Q: Solve the initial value problem. Y 6 dy dx 2xy = 8x, y(0) = 5

A:

Q: dy 6. Solve the initial value problem y(0) = –2. %3D - dx

A:

Q: Solve the initial value problem. dy 2xy = 8x, у(0) — 0 dx y =

A:

Q: Solve the initial-value problem dy + dx 2 e* + 1 \x – 1/ (х — 1)2 y(0) = 2

A: Given: dydx+2x−1y=ex+1(x−1)2

Q: // Solve the initial value Problem xdy - (y+y) dx 0,y(1) = 1. |

A: According to the given information, it is required to solve the given initial value problem.

Q: dy Solve the Initial Value Problem: X- dx +y=x°y* subject to y(1)= 2.

A: Given: xdydx+y=x3y4 , y(1)=2 rewrite given equation dydx+yx=x2y4      Bernouli's…