Internal problem ID [9014]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 679.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class D`], _Riccati]
\[ \boxed {y^{\prime }-\frac {y+x^{3} \ln \left (x \right )+x^{4}+x^{3}+7 x y^{2} \ln \left (x \right )+7 y^{2} x^{2}+7 x y^{2}}{x}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 37
dsolve(diff(y(x),x) = (y(x)+x^3*ln(x)+x^4+x^3+7*x*y(x)^2*ln(x)+7*x^2*y(x)^2+7*x*y(x)^2)/x,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\tan \left (\frac {\left (6 \ln \left (x \right ) x^{2}+4 x^{3}+3 x^{2}+12 c_{1} \right ) \sqrt {7}}{12}\right ) x \sqrt {7}}{7} \]
✓ Solution by Mathematica
Time used: 0.419 (sec). Leaf size: 44
DSolve[y'[x] == (x^3 + x^4 + x^3*Log[x] + y[x] + 7*x*y[x]^2 + 7*x^2*y[x]^2 + 7*x*Log[x]*y[x]^2)/x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x \tan \left (\frac {1}{12} \sqrt {7} \left (4 x^3+3 x^2+6 x^2 \log (x)+12 c_1\right )\right )}{\sqrt {7}} \]