75.6.24 problem 157

Internal problem ID [16780]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 6. Linear equations of the first order. The Bernoulli equation. Exercises page 54
Problem number : 157
Date solved : Tuesday, January 28, 2025 at 09:22:22 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 14

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

\[ y = \frac {1}{{\mathrm e}^{x^{2}} c_{1} +1} \]

✓ Solution by Mathematica

Time used: 0.262 (sec). Leaf size: 42

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

\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{(K[1]-1) K[1]}dK[1]\&\right ]\left [x^2+c_1\right ] \\ y(x)\to 0 \\ y(x)\to 1 \\ \end{align*}