Answer to Question #245836 in Differential Equations for Gabriel

Question

dP/dt+2tP=P4t-2

Answer 1

Solution:

$dp/dt+2tp=p+4t-2$

$dp/dt=p+4t-2-2tp=(2-p)(-1+2t)$

$dp/dt=(2-p)(-1+2t)$

$\int dp/(2-p)=\int(-1+2t)dt$

$-ln (2-p)=-t+t^2+C_3$

$2-p=exp(t-t^2+C_2)=C_1exp(t-t^2), C_2=-C_3, C_1=exp(C_2)$

$p(t)=Cexp(t-t^2)+2, C=-C_1$