29.29.31 problem 853

Internal problem ID [5436]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 29
Problem number : 853
Date solved : Monday, January 27, 2025 at 11:23:32 AM
CAS classification : [[_homogeneous, `class G`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.057 (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 x \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 )}{3 \left (y \left (x \right )-\sqrt {-4 a x +y \left (x \right )^{2}}\right )^{2}} &= 0 \\ -\frac {8 \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 ) x}{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: 60.299 (sec). Leaf size: 4845

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

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