29.29.14 problem 836

Internal problem ID [5419]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 29
Problem number : 836
Date solved : Monday, January 27, 2025 at 11:21:40 AM
CAS classification : [[_homogeneous, `class G`]]

\begin{align*} 3 {y^{\prime }}^{2}+4 x y^{\prime }+x^{2}-y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.041 (sec). Leaf size: 93

dsolve(3*diff(y(x),x)^2+4*x*diff(y(x),x)+x^2-y(x) = 0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 3.960 (sec). Leaf size: 121

DSolve[3 (D[y[x],x])^2+4 x D[y[x],x]+x^2-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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