2 y- 10 sinix) a) Solve the first order li ear differential equation dy 12x'y x. dx dy y b) Solve the first order homogeneous differential equation dx given y(1)-2. d'y c) Solve the second order differential equation y 10 sinix) dx dx

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Chapter1: Functions And Models
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Question
2 y- 10 sinix)
a) Solve the first order li ear differential equation
dy
12x'y x.
dx
dy y
b) Solve the first order homogeneous differential equation
dx
given y(1)-2.
d'y
c) Solve the second order differential equation
y 10 sinix)
dx
dx
Transcribed Image Text:2 y- 10 sinix) a) Solve the first order li ear differential equation dy 12x'y x. dx dy y b) Solve the first order homogeneous differential equation dx given y(1)-2. d'y c) Solve the second order differential equation y 10 sinix) dx dx
Expert Solution
Step 1

“Since you have asked multiple question, we will solve the first question for you. If you want any specific question to be solved then please specify the question number or post only that question.” 

 

Solving:

 

First order Linear Differential equation :

                                            dydx-12x3y=x3

 

Solution:

                             This is the first order separable ODE of the form : N(y) . y'=M(x)

                                                                    

                                       

                          

Step 2

Hence,

                 Re-writing it in the separable form:

                                            dydx=x3 + 12x3ydydx=x31 + 12ydy(1+12y)=x3 dx

 

Taking Integration on both sides, we get :

                                            dy1+12y= x3 dxUsing u-substitution rule:Let      u=1+12y         du=12 dy         dy=112du

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