60.2.140 problem 716

Internal problem ID [10727]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 716
Date solved : Tuesday, January 28, 2025 at 05:08:53 PM
CAS classification : [_rational]

\begin{align*} y^{\prime }&=\frac {3 x^{4}+3 x^{3}+\sqrt {9 x^{4}-4 y^{3}}}{\left (1+x \right ) y^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.045 (sec). Leaf size: 37

dsolve(diff(y(x),x) = (3*x^4+3*x^3+(9*x^4-4*y(x)^3)^(1/2))/(x+1)/y(x)^2,y(x), singsol=all)
 

\[ \int _{\textit {\_b}}^{y}\frac {\textit {\_a}^{2}}{\sqrt {9 x^{4}-4 \textit {\_a}^{3}}}d \textit {\_a} -\ln \left (x +1\right )-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 3.349 (sec). Leaf size: 133

DSolve[D[y[x],x] == (3*x^3 + 3*x^4 + Sqrt[9*x^4 - 4*y[x]^3])/((1 + x)*y[x]^2),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \left (-\frac {3}{2}\right )^{2/3} \sqrt [3]{x^4-4 \log ^2(x+1)+8 c_1 \log (x+1)-4 c_1{}^2} \\ y(x)\to \left (\frac {3}{2}\right )^{2/3} \sqrt [3]{x^4-4 \log ^2(x+1)+8 c_1 \log (x+1)-4 c_1{}^2} \\ y(x)\to -\sqrt [3]{-1} \left (\frac {3}{2}\right )^{2/3} \sqrt [3]{x^4-4 \log ^2(x+1)+8 c_1 \log (x+1)-4 c_1{}^2} \\ \end{align*}