60.2.101 problem 677

Internal problem ID [10688]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 677
Date solved : Monday, January 27, 2025 at 09:26:40 PM
CAS classification : [[_homogeneous, `class D`], _Riccati]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 48

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

\[ y = \tanh \left (\frac {\sqrt {a}\, \left (6 \ln \left (x +1\right ) x^{2}+4 x^{3}+3 x^{2}-6 \ln \left (x +1\right )+12 c_{1} +6 x +9\right )}{12}\right ) x \sqrt {a} \]

✓ Solution by Mathematica

Time used: 0.154 (sec). Leaf size: 57

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

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {1}{a-K[1]^2}dK[1]=\frac {1}{12} \left (x \left (4 x^2+3 x+6\right )+6 \left (x^2-1\right ) \log (x+1)\right )+c_1,y(x)\right ] \]