15.4.14 problem 15

Internal problem ID [2927]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 8, page 34
Problem number : 15
Date solved : Monday, January 27, 2025 at 06:56:54 AM
CAS classification : [[_homogeneous, `class G`], _exact, _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.046 (sec). Leaf size: 57

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

\begin{align*} y &= \frac {c_1^{3}-\sqrt {c_1^{6}+4 c_1 \,x^{5}}}{2 x^{3} c_1^{3}} \\ y &= \frac {c_1^{3}+\sqrt {c_1^{6}+4 c_1 \,x^{5}}}{2 c_1^{3} x^{3}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 1.149 (sec). Leaf size: 80

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

\begin{align*} y(x)\to \frac {1-\sqrt {\frac {1}{x^3}} x^2 \sqrt {\frac {1}{x}+4 c_1 x^4}}{2 x^3} \\ y(x)\to \frac {1+\sqrt {\frac {1}{x^3}} x^2 \sqrt {\frac {1}{x}+4 c_1 x^4}}{2 x^3} \\ \end{align*}