20.1.24 problem Problem 32

Internal problem ID [3581]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.2, Basic Ideas and Terminology. page 21
Problem number : Problem 32
Date solved : Monday, January 27, 2025 at 07:46:08 AM
CAS classification : [_Bernoulli]

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

With initial conditions

\begin{align*} y \left (\pi \right )&=\frac {1}{\pi } \end{align*}

✓ Solution by Maple

Time used: 0.162 (sec). Leaf size: 14

dsolve([diff(y(x),x)=(cos(x)-2*x*y(x)^2)/(2*x^2*y(x)),y(Pi) = 1/Pi],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.287 (sec). Leaf size: 17

DSolve[{D[y[x],x]==(Cos[x]-2*x*y[x]^2)/(2*x^2*y[x]),{y[Pi]==1/Pi}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\sqrt {\sin (x)+1}}{x} \]