Internal problem ID [8711]
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]
\[ \boxed {{y^{\prime }}^{2}+a y^{\prime }=-x b} \]
✓ Solution by Maple
Time used: 0.047 (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 )^{\frac {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[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*}