20.3.17 problem Problem 17

Internal problem ID [3626]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.6, First-Order Linear Differential Equations. page 59
Problem number : Problem 17
Date solved : Sunday, March 30, 2025 at 01:54:50 AM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (\frac {\pi }{2}\right )&=2 \end{align*}

✓ Maple. Time used: 0.025 (sec). Leaf size: 13

ode:=sin(x)*diff(y(x),x)-y(x)*cos(x) = sin(2*x); 
ic:=y(1/2*Pi) = 2; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = 2 \left (\ln \left (\sin \left (x \right )\right )+1\right ) \sin \left (x \right ) \]

✓ Mathematica. Time used: 0.039 (sec). Leaf size: 14

ode=Sin[x]*D[y[x],x]-y[x]*Cos[x]==Sin[2*x]; 
ic={y[Pi/2]==2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to 2 \sin (x) (\log (\sin (x))+1) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x)*cos(x) + sin(x)*Derivative(y(x), x) - sin(2*x),0) 
ics = {y(pi/2): 2} 
dsolve(ode,func=y(x),ics=ics)
 

ValueError : Couldnt solve for initial conditions