Internal problem ID [4048]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 28
Problem number: 809.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]
\[ \boxed {{y^{\prime }}^{2}-y y^{\prime }=-{\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.282 (sec). Leaf size: 30
dsolve(diff(y(x),x)^2-y(x)*diff(y(x),x)+exp(x) = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = -2 \,{\mathrm e}^{\frac {x}{2}} y \left (x \right ) = 2 \,{\mathrm e}^{\frac {x}{2}} y \left (x \right ) = \frac {1}{c_{1}}+c_{1} {\mathrm e}^{x} \end{align*}
✓ Solution by Mathematica
Time used: 60.35 (sec). Leaf size: 59
DSolve[(y'[x])^2-y[x] y'[x]+Exp[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {-e^{-c_1} \left (-e^x+e^{c_1}\right ){}^2} y(x)\to \sqrt {-e^{-c_1} \left (e^x-e^{c_1}\right ){}^2} \end{align*}