29.15.5 problem 413

Internal problem ID [5011]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 15
Problem number : 413
Date solved : Sunday, March 30, 2025 at 04:30:51 AM
CAS classification : [_separable]

\begin{align*} \left (\cos \left (x \right )-\sin \left (x \right )\right ) y^{\prime }+y \left (\cos \left (x \right )+\sin \left (x \right )\right )&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 13

ode:=(cos(x)-sin(x))*diff(y(x),x)+y(x)*(cos(x)+sin(x)) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \left (\cos \left (x \right )-\sin \left (x \right )\right ) \]

✓ Mathematica. Time used: 0.114 (sec). Leaf size: 20

ode=(Cos[x]-Sin[x])D[y[x],x]+y[x](Cos[x]+Sin[x])==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.703 (sec). Leaf size: 17

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

\[ y{\left (x \right )} = \frac {C_{1}}{\sqrt {\tan ^{2}{\left (x + \frac {\pi }{4} \right )} + 1}} \]