77.1.27 problem 43 (page 55)

Internal problem ID [17917]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 43 (page 55)
Date solved : Tuesday, January 28, 2025 at 11:12:26 AM
CAS classification : [_rational, _Riccati]

\begin{align*} x y^{\prime }-3 y+y^{2}&=4 x^{2}-4 x \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 46

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

\[ y = -\frac {2 x \left (8 c_{1} x^{2}-{\mathrm e}^{4 x}-4 c_{1} x -c_{1} \right )}{{\mathrm e}^{4 x}+c_{1} \left (8 x^{2}+4 x +1\right )} \]

✓ Solution by Mathematica

Time used: 0.248 (sec). Leaf size: 55

DSolve[x*D[y[x],x]-3*y[x]+y[x]^2==4*x^2-4*x,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {2 x \left (8 x^2-4 x+32 c_1 e^{4 x}-1\right )}{8 x^2+4 x-32 c_1 e^{4 x}+1} \\ y(x)\to 2 x \\ \end{align*}