29.27.11 problem 777

Internal problem ID [5361]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 27
Problem number : 777
Date solved : Monday, January 27, 2025 at 11:17:19 AM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{2}+a y^{\prime }+b&=0 \end{align*}

✓ Solution by Maple

Time used: 0.041 (sec). Leaf size: 43

dsolve(diff(y(x),x)^2+a*diff(y(x),x)+b = 0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= -\frac {a x}{2}-\frac {x \sqrt {a^{2}-4 b}}{2}+c_{1} \\ y \left (x \right ) &= -\frac {a x}{2}+\frac {x \sqrt {a^{2}-4 b}}{2}+c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 59

DSolve[(D[y[x],x])^2+a*D[y[x],x]+b==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {1}{2} x \sqrt {a^2-4 b}-\frac {a x}{2}+c_1 \\ y(x)\to \frac {1}{2} x \sqrt {a^2-4 b}-\frac {a x}{2}+c_1 \\ \end{align*}