Internal problem ID [4092]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 29
Problem number: 853.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class G`], _dAlembert]
\[ \boxed {{y^{\prime }}^{2} x +y y^{\prime }=-a} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 177
dsolve(x*diff(y(x),x)^2+y(x)*diff(y(x),x)+a = 0,y(x), singsol=all)
\begin{align*} -\frac {8 \left (-\frac {3 c_{1} \left (y \left (x \right )-\sqrt {-4 a x +y \left (x \right )^{2}}\right ) \sqrt {\frac {-y \left (x \right )+\sqrt {-4 a x +y \left (x \right )^{2}}}{x}}}{8}+a x -\frac {3 y \left (x \right )^{2}}{4}+\frac {3 y \left (x \right ) \sqrt {-4 a x +y \left (x \right )^{2}}}{4}\right ) x}{3 \left (y \left (x \right )-\sqrt {-4 a x +y \left (x \right )^{2}}\right )^{2}} &= 0 \\ -\frac {8 x \left (\frac {3 c_{1} \left (y \left (x \right )+\sqrt {-4 a x +y \left (x \right )^{2}}\right ) \sqrt {\frac {-2 y \left (x \right )-2 \sqrt {-4 a x +y \left (x \right )^{2}}}{x}}}{4}+a x -\frac {3 y \left (x \right )^{2}}{4}-\frac {3 y \left (x \right ) \sqrt {-4 a x +y \left (x \right )^{2}}}{4}\right )}{3 \left (y \left (x \right )+\sqrt {-4 a x +y \left (x \right )^{2}}\right )^{2}} &= 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 60.29 (sec). Leaf size: 4845
DSolve[x (y'[x])^2+y[x] y'[x]+a==0,y[x],x,IncludeSingularSolutions -> True]
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