Internal problem ID [67]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.5. Linear first order equations. Page 56
Problem number: 14.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {-3 y+y^{\prime } x -x^{3}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 10] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 12
dsolve([-3*y(x)+x*diff(y(x),x) = x^3,y(1) = 10],y(x), singsol=all)
\[ y \relax (x ) = \left (\ln \relax (x )+10\right ) x^{3} \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 13
DSolve[{-3*y[x]+x*y'[x] == x^3,y[1]==10},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^3 (\log (x)+10) \\ \end{align*}