83.18.4 problem 4

Internal problem ID [19214]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter IV. Equations of the first order but not of the first degree. Exercise IV (A) at page 53
Problem number : 4
Date solved : Tuesday, January 28, 2025 at 01:13:52 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 21

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

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 29

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

\begin{align*} y(x)\to -\frac {3 x^2}{2}+c_1 \\ y(x)\to \frac {x^2}{2}+c_1 \\ \end{align*}