15.7.11 problem 11

Internal problem ID [2992]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 11, page 45
Problem number : 11
Date solved : Monday, January 27, 2025 at 07:06:01 AM
CAS classification : [_Bernoulli]

\begin{align*} y+x y^{\prime }&=y^{2} x^{2} \cos \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 16

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

\[ y = \frac {1}{\left (-\sin \left (x \right )+c_{1} \right ) x} \]

✓ Solution by Mathematica

Time used: 0.208 (sec). Leaf size: 22

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

\begin{align*} y(x)\to \frac {1}{-x \sin (x)+c_1 x} \\ y(x)\to 0 \\ \end{align*}