75.6.25 problem 158

Internal problem ID [16781]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 6. Linear equations of the first order. The Bernoulli equation. Exercises page 54
Problem number : 158
Date solved : Tuesday, January 28, 2025 at 09:22:24 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 55

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

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

✓ Solution by Mathematica

Time used: 0.204 (sec). Leaf size: 66

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

\begin{align*} y(x)\to x^{2/3} \sqrt [3]{x+c_1} \\ y(x)\to -\sqrt [3]{-1} x^{2/3} \sqrt [3]{x+c_1} \\ y(x)\to (-1)^{2/3} x^{2/3} \sqrt [3]{x+c_1} \\ \end{align*}