60.2.11 problem 587

Internal problem ID [10598]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 587
Date solved : Tuesday, January 28, 2025 at 04:55:32 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`]]

\begin{align*} y^{\prime }&=\frac {\left (x^{{3}/{2}}+2 F \left (y-\frac {x^{3}}{6}\right )\right ) \sqrt {x}}{2} \end{align*}

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 29

dsolve(diff(y(x),x) = 1/2*(x^(3/2)+2*F(y(x)-1/6*x^3))*x^(1/2),y(x), singsol=all)
 

\[ \int _{\textit {\_b}}^{y}\frac {1}{F \left (\textit {\_a} -\frac {x^{3}}{6}\right )}d \textit {\_a} -\frac {2 x^{{3}/{2}}}{3}-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.241 (sec). Leaf size: 123

DSolve[D[y[x],x] == (Sqrt[x]*(x^(3/2) + 2*F[-1/6*x^3 + y[x]]))/2,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{y(x)}-\frac {F\left (K[2]-\frac {x^3}{6}\right ) \int _1^x-\frac {K[1]^2 F''\left (K[2]-\frac {K[1]^3}{6}\right )}{2 F\left (K[2]-\frac {K[1]^3}{6}\right )^2}dK[1]+1}{F\left (K[2]-\frac {x^3}{6}\right )}dK[2]+\int _1^x\left (\frac {K[1]^2}{2 F\left (y(x)-\frac {K[1]^3}{6}\right )}+\sqrt {K[1]}\right )dK[1]=c_1,y(x)\right ] \]