60.1.166 problem 167

Internal problem ID [10180]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 167
Date solved : Monday, January 27, 2025 at 06:31:32 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Riccati]

\begin{align*} 3 x^{2} y^{\prime }-7 y^{2}-3 y x -x^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 20

dsolve(3*x^2*diff(y(x),x) - 7*y(x)^2 - 3*x*y(x) - x^2=0,y(x), singsol=all)
 

\[ y = \frac {\tan \left (\frac {\left (\ln \left (x \right )+c_{1} \right ) \sqrt {7}}{3}\right ) x \sqrt {7}}{7} \]

✓ Solution by Mathematica

Time used: 0.077 (sec). Leaf size: 35

DSolve[3*x^2*D[y[x],x] - 7*y[x]^2 - 3*x*y[x] - x^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {1}{7 K[1]^2+1}dK[1]=\frac {\log (x)}{3}+c_1,y(x)\right ] \]