Internal problem ID [3539]
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]]
\[ \boxed {{y^{\prime }}^{2}-y y^{\prime }+{\mathrm e}^{x}=0} \]
✓ 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: 60.215 (sec). Leaf size: 57
DSolve[(y'[x])^2-y[x] y'[x]+Exp[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -2 \sqrt {-e^x \sinh ^2\left (\frac {x-c_1}{2}\right )} \\ y(x)\to 2 \sqrt {-e^x \sinh ^2\left (\frac {x-c_1}{2}\right )} \\ \end{align*}