Internal problem ID [2511]
Book: Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section: Exercises, page 14
Problem number: 2(i).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime } x +2 y-\left (3 x +2\right ) {\mathrm e}^{3 x}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 19
dsolve([x*diff(y(x),x)+2*y(x)=(3*x+2)*exp(3*x),y(1) = 1],y(x), singsol=all)
\[ y \relax (x ) = \frac {x^{2} {\mathrm e}^{3 x}-{\mathrm e}^{3}+1}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.087 (sec). Leaf size: 22
DSolve[{x*y'[x]+2*y[x]==(3*x+2)*Exp[3*x],y[1]==1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1-e^3}{x^2}+e^{3 x} \\ \end{align*}