Find the General and Particular solution of ????= −8 sin 4? ; ? = 6 ?ℎ?? ? = 0 ax ay a 0y" = 12x?y' = 4x3 + C1y = x* + C1x+ C2 → General SolutionFor the Constant, C,: when x = 0, y' = 22 = 4x3 + CC = 2For the Constant, C2: when x = 0, y = 11 = 0 + 2(0) + C2C, = -1y = x* + 2x + -1 → Particular Solutionof and for the exclusive use of SLU. Reproduction, storing in a retrieval system, distributing, uploading or posting online, or transmitting in any form or by any 2electronic, mechanical, photocopying, recording, or otherwise of any part of this document, without the prior written permission of SLU, is strictly prohibited.***OEVALUATEThe following problems are given to assess your ability to solve for the solutions ofdifferential equationsInstructions: Solve for what is asked in each problem. Refer to the format and guidelinespresented in the Assignment Guide.1. Complete the table below.Ordinary orPartialDependentVariableOrder DegreeLinear or Non-LinearIndependentVariabley' = x +6yy" = 4y +y(d?y\dy(dz) + dx+ 3 = 0y" +2xy' +4y =cos2xx²-1dx y+4aw+dydu= 0ax2. Verify that the function y = Ciex + Cex is a solution of the differentialequation y" - 3y' + 2y = 03. Is y(x) = Cisin2x + C2cos2x, where Ci and C2 are arbitrary constants, a solutionof y" + 4y = 0?4. Find the General and Particular solution of = -8 sin 4x ; y = 6 when x = 0dx5. Find the General and Particular solution of = 3y ; y = 3, when x = 0dx• For students who are on the online mode, detailed instructions are provided in yourGOOGLE CLASSROOM which will guide you in utilizing learning materials, performinglearning activities, accomplishing requirements, and formatting/ saving reports andoutputs for ONLINE submissionof and for the exclusive use of SLU. Reproduction, storing in a retrieval system, distributing, uploading or posting online, or transmitting in any form or by anyelectronic, mechanical, photocopying, recording, or otherwise of any part of this document, without the prior written permission of SLU, is strictly prohibited.EX

Question

Find the General and Particular solution of ????= −8 sin 4? ; ? = 6 ?ℎ?? ? = 0 ax ay a 0y&#34; = 12x?y' = 4x3 + C1y = x* + C1x+ C2 → General SolutionFor the Constant, C,: when x = 0, y' = 22 = 4x3 + CC = 2For the Constant, C2: when x = 0, y = 11 = 0 + 2(0) + C2C, = -1y = x* + 2x + -1 → Particular Solutionof and for the exclusive use of SLU. Reproduction, storing in a retrieval system, distributing, uploading or posting online, or transmitting in any form or by any 2electronic, mechanical, photocopying, recording, or otherwise of any part of this document, without the prior written permission of SLU, is strictly prohibited.***OEVALUATEThe following problems are given to assess your ability to solve for the solutions ofdifferential equationsInstructions: Solve for what is asked in each problem. Refer to the format and guidelinespresented in the Assignment Guide.1. Complete the table below.Ordinary orPartialDependentVariableOrder DegreeLinear or Non-LinearIndependentVariabley' = x +6yy&#34; = 4y +y(d?y\dy(dz) + dx+ 3 = 0y&#34; +2xy' +4y =cos2xx²-1dx y+4aw+dydu= 0ax2. Verify that the function y = Ciex + Cex is a solution of the differentialequation y&#34; - 3y' + 2y = 03. Is y(x) = Cisin2x + C2cos2x, where Ci and C2 are arbitrary constants, a solutionof y&#34; + 4y = 0?4. Find the General and Particular solution of = -8 sin 4x ; y = 6 when x = 0dx5. Find the General and Particular solution of = 3y ; y = 3, when x = 0dx• For students who are on the online mode, detailed instructions are provided in yourGOOGLE CLASSROOM which will guide you in utilizing learning materials, performinglearning activities, accomplishing requirements, and formatting/ saving reports andoutputs for ONLINE submissionof and for the exclusive use of SLU. Reproduction, storing in a retrieval system, distributing, uploading or posting online, or transmitting in any form or by anyelectronic, mechanical, photocopying, recording, or otherwise of any part of this document, without the prior written permission of SLU, is strictly prohibited.EX

Accepted Answer

Given- dydx=-8sin4x
To Find- The general and particular solution of the above differential equation…

4. Find the General and Particular solution of = -8 sin 4x; y= 6 when x = 0