I need helpSolve the following first order differential equation:3tx′−2x=t3x2

Mary Keefe

Mary Keefe

Answered

2022-01-19

I need help
Solve the following first order differential equation:
3tx2x=t3x2

Answer & Explanation

Dabanka4v

Dabanka4v

Expert

2022-01-19Added 36 answers

Given
3tx2x=t3x2
3tdxdt2x=t3x2
dxdt2x3t=t3x23t
dxdt2x3t=t23x2
x2dxdt2x33t=t2v
3x2dxdt2x3t=3t2
Let x3=u
3x2dxdt=dudt
dudt2tu=et2
dudt+Pu=Q where
P=2t;  Q=3t2
If=ePdt=e2tdt=e2lnt=1t2
Solution:
u(If)=Q(If)dt+c
x31t2=3t21t2dt+c=3t+c
x3t2=3t+c

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