Internal problem ID [917]
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: 31.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {2 y+y^{\prime } x -8 x^{2}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve([x*diff(y(x),x)+2*y(x)=8*x^2,y(1) = 3],y(x), singsol=all)
\[ y \relax (x ) = \frac {2 x^{4}+1}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.028 (sec). Leaf size: 14
DSolve[{x*y'[x]+2*y[x]==8*x^2,y[1]==3},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 2 x^2+\frac {1}{x^2} \\ \end{align*}