29.28.11 problem 809

Internal problem ID [5392]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 28
Problem number : 809
Date solved : Monday, January 27, 2025 at 11:17:55 AM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} {y^{\prime }}^{2}-y^{\prime } y+{\mathrm e}^{x}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.610 (sec). Leaf size: 34

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 {c_{1}^{2} {\mathrm e}^{x}+1}{c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 9.657 (sec). Leaf size: 163

DSolve[(D[y[x],x])^2-y[x]*D[y[x],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*}