Internal problem ID [50]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.4. Separable equations. Page 43
Problem number: 25.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {-y+y^{\prime } x -2 x^{2} y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 12
dsolve([-y(x)+x*diff(y(x),x) = 2*x^2*y(x),y(1) = 1],y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\left (x -1\right ) \left (x +1\right )} x \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 14
DSolve[{-y[x]+x*y'[x] == 2*x^2*y[x],y[1]==1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{x^2-1} x \\ \end{align*}