Internal problem ID [5299]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 6. Equations of first order and first degree (Linear equations). Supplemetary
problems. Page 39
Problem number: 19 (c).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-y-x y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 13
dsolve(diff(y(x),x)-y(x)=x*y(x),y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{\frac {x \left (x +2\right )}{2}} \]
✓ Solution by Mathematica
Time used: 0.024 (sec). Leaf size: 23
DSolve[y'[x]-y[x]==x*y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{\frac {1}{2} x (x+2)} \\ y(x)\to 0 \\ \end{align*}