Internal problem ID [7955]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 375.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}+a y^{\prime }+x b=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 49
dsolve(diff(y(x),x)^2+a*diff(y(x),x)+b*x = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {x a}{2}+\frac {\left (a^{2}-4 b x \right )^{\frac {3}{2}}}{12 b}+c_{1} \\ y \relax (x ) = -\frac {x a}{2}-\frac {\left (a^{2}-4 b x \right )^{\frac {3}{2}}}{12 b}+c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 68
DSolve[b*x + a*y'[x] + y'[x]^2==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*}