67.2.59 problem Problem 20(f)

Internal problem ID [13945]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 4, Second and Higher Order Linear Differential Equations. Problems page 221
Problem number : Problem 20(f)
Date solved : Monday, March 31, 2025 at 08:19:49 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (2 \sin \left (x \right )-\cos \left (x \right )\right ) y^{\prime \prime }+\left (7 \sin \left (x \right )+4 \cos \left (x \right )\right ) y^{\prime }+10 y \cos \left (x \right )&=0 \end{align*}

✓ Maple. Time used: 0.249 (sec). Leaf size: 74

ode:=(2*sin(x)-cos(x))*diff(diff(y(x),x),x)+(7*sin(x)+4*cos(x))*diff(y(x),x)+10*cos(x)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-\int \frac {5 \cos \left (x \right ) \cot \left (x \right )-6 \csc \left (x \right )}{\cos \left (x \right )-2 \sin \left (x \right )}d x} \left (c_1 -c_2 \int \frac {{\mathrm e}^{\int \frac {5 \cos \left (x \right ) \cot \left (x \right )-6 \csc \left (x \right )}{\cos \left (x \right )-2 \sin \left (x \right )}d x} \csc \left (x \right )}{\cos \left (x \right )-2 \sin \left (x \right )}d x \right ) \]

✓ Mathematica. Time used: 1.451 (sec). Leaf size: 157

ode=(2*Sin[x]-Cos[x])*D[y[x],{x,2}]+(7*Sin[x]+4*Cos[x])*D[y[x],x]+10*y[x]*Cos[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \exp \left (\int _1^{e^{i x}}\frac {(4+3 i) K[1]^2+(5-5 i)}{5 K[1]-(3-4 i) K[1]^3}dK[1]-\frac {1}{2} \int _1^{e^{i x}}\frac {(8+6 i) K[2]^2-(6-2 i)}{K[2] \left ((1+2 i) K[2]^2+(1-2 i)\right )}dK[2]\right ) \left (c_2 \int _1^{e^{i x}}\exp \left (-2 \int _1^{K[3]}\frac {(4+3 i) K[1]^2+(5-5 i)}{5 K[1]-(3-4 i) K[1]^3}dK[1]\right )dK[3]+c_1\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((2*sin(x) - cos(x))*Derivative(y(x), (x, 2)) + (7*sin(x) + 4*cos(x))*Derivative(y(x), x) + 10*y(x)*cos(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False