Internal problem ID [918]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Linear first order. Section 2.1 Page 41
Problem number: 32.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime } x -2 y+x^{2}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.009 (sec). Leaf size: 14
dsolve([x*diff(y(x),x)-2*y(x)=-x^2,y(1) = 1],y(x), singsol=all)
\[ y \relax (x ) = \left (-\ln \relax (x )+1\right ) x^{2} \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 14
DSolve[{x*y'[x]-2*y[x]==-x^2,y[1]==1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x^2 (\log (x)-1) \\ \end{align*}