Internal problem ID [3020]
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]
\[ \boxed {x y^{\prime }+2 y=\left (2+3 x \right ) {\mathrm e}^{3 x}} \] With initial conditions \begin {align*} [y \left (1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.047 (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)
\[ y \left (x \right ) = \frac {x^{2} {\mathrm e}^{3 x}-{\mathrm e}^{3}+1}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.086 (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]
\[ y(x)\to -\frac {e^3}{x^2}+\frac {1}{x^2}+e^{3 x} \]