60.2.280 problem 856

Internal problem ID [10867]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 856
Date solved : Tuesday, January 28, 2025 at 05:26:48 PM
CAS classification : [NONE]

\begin{align*} y^{\prime }&=-\frac {\left (-\frac {1}{x}-\textit {\_F1} \left (y^{2}-2 x \right )\right ) x}{\sqrt {y^{2}}} \end{align*}

✓ Solution by Maple

Time used: 0.128 (sec). Leaf size: 65

dsolve(diff(y(x),x) = -(-1/x-_F1(y(x)^2-2*x))/(y(x)^2)^(1/2)*x,y(x), singsol=all)
 

\begin{align*} y &= \sqrt {2 \operatorname {RootOf}\left (x^{2}-2 \left (\int _{}^{\textit {\_Z}}\frac {1}{f_{1} \left (2 \textit {\_a} \right )}d \textit {\_a} \right )+4 c_{1} \right )+2 x} \\ y &= -\sqrt {2 \operatorname {RootOf}\left (x^{2}-2 \left (\int _{}^{\textit {\_Z}}\frac {1}{f_{1} \left (2 \textit {\_a} \right )}d \textit {\_a} \right )+4 c_{1} \right )+2 x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.308 (sec). Leaf size: 99

DSolve[D[y[x],x] == (x*(x^(-1) + F1[-2*x + y[x]^2]))/Sqrt[y[x]^2],y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{y(x)}\left (\frac {\sqrt {K[2]^2}}{\text {F1}\left (K[2]^2-2 x\right )}-\int _1^x\frac {2 K[2] \text {F1}''\left (K[2]^2-2 K[1]\right )}{\text {F1}\left (K[2]^2-2 K[1]\right )^2}dK[1]\right )dK[2]+\int _1^x\left (-K[1]-\frac {1}{\text {F1}\left (y(x)^2-2 K[1]\right )}\right )dK[1]=c_1,y(x)\right ] \]