64.4.9 problem 9

Internal problem ID [13298]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.2 (Separable equations). Exercises page 47
Problem number : 9
Date solved : Tuesday, January 28, 2025 at 05:16:26 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} 2 y x +3 y^{2}-\left (2 y x +x^{2}\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.055 (sec). Leaf size: 33

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

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

✓ Solution by Mathematica

Time used: 0.137 (sec). Leaf size: 38

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

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {2 K[1]+1}{K[1] (K[1]+1)}dK[1]=\log (x)+c_1,y(x)\right ] \]