69.1.59 problem 78

Internal problem ID [14212]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 78
Date solved : Tuesday, January 28, 2025 at 06:22:11 AM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, _Bernoulli]

\begin{align*} \frac {1}{x^{2}}+\frac {3 y^{2}}{x^{4}}&=\frac {2 y y^{\prime }}{x^{3}} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 26

dsolve(1/x^2+ 3*y(x)^2/x^4=2*y(x)/x^3*diff(y(x),x),y(x), singsol=all)
 

\begin{align*} y &= \sqrt {c_{1} x -1}\, x \\ y &= -\sqrt {c_{1} x -1}\, x \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.288 (sec). Leaf size: 34

DSolve[1/x^2+ 3*y[x]^2/x^4==2*y[x]/x^3*D[y[x],x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -x \sqrt {-1+c_1 x} \\ y(x)\to x \sqrt {-1+c_1 x} \\ \end{align*}