76.1.17 problem 17

Internal problem ID [17316]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.1 (Separable equations). Problems at page 44
Problem number : 17
Date solved : Tuesday, January 28, 2025 at 09:59:48 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=-7 \end{align*}

✓ Solution by Maple

Time used: 0.108 (sec). Leaf size: 18

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

\[ y = -\sqrt {3 \ln \left (x^{2}+1\right )+49} \]

✓ Solution by Mathematica

Time used: 0.111 (sec). Leaf size: 21

DSolve[{D[y[x],x]==3*x/(y[x]+x^2*y[x]),{y[0]==-7}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\sqrt {3 \log \left (x^2+1\right )+49} \]