Internal problem ID [3540]
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]]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}-y^{\prime } y+{\mathrm e}^{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.375 (sec). Leaf size: 21
dsolve(diff(y(x),x)^2-y(x)*diff(y(x),x)+exp(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {1}{c_{1}}+c_{1} {\mathrm e}^{x} \\ y \relax (x ) = c_{1} {\mathrm e}^{\frac {x}{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 12.899 (sec). Leaf size: 163
DSolve[(y'[x])^2-y[x] y'[x]+Exp[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {2 i e^{x/2}}{\sqrt {-1+\tanh ^2\left (\frac {x-c_1}{2}\right )}} \\ y(x)\to \frac {2 i e^{x/2}}{\sqrt {-1+\tanh ^2\left (\frac {x-c_1}{2}\right )}} \\ y(x)\to -\frac {2 i e^{x/2}}{\sqrt {-1+\tanh ^2\left (\frac {-x+c_1}{2}\right )}} \\ y(x)\to \frac {2 i e^{x/2}}{\sqrt {-1+\tanh ^2\left (\frac {-x+c_1}{2}\right )}} \\ y(x)\to -2 e^{x/2} \\ y(x)\to 2 e^{x/2} \\ \end{align*}