29.27.12 problem 778

Internal problem ID [5362]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 27
Problem number : 778
Date solved : Monday, January 27, 2025 at 11:17:19 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.035 (sec). Leaf size: 70

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

\begin{align*} y \left (x \right ) &= \frac {\left (a^{2}-4 b x \right )^{{3}/{2}}-6 b \left (a x -2 c_{1} \right )}{12 b} \\ y \left (x \right ) &= \frac {\left (-a^{2}+4 b x \right ) \sqrt {a^{2}-4 b x}-6 b \left (a x -2 c_{1} \right )}{12 b} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 68

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

\begin{align*} y(x)\to -\frac {\left (a^2-4 b x\right )^{3/2}+6 a b x}{12 b}+c_1 \\ y(x)\to \frac {1}{2} \left (\frac {\left (a^2-4 b x\right )^{3/2}}{6 b}-a x\right )+c_1 \\ \end{align*}