38.1.1 problem 1

Internal problem ID [8162]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Exercises 1.1 at page 12
Problem number : 1
Date solved : Friday, October 03, 2025 at 02:13:04 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} \left (1-x \right ) y^{\prime \prime }-4 x y^{\prime }+5 y&=\cos \left (x \right ) \end{align*}

✓ Maple. Time used: 0.380 (sec). Leaf size: 337

ode:=(1-x)*diff(diff(y(x),x),x)-4*x*diff(y(x),x)+5*y(x) = cos(x); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Mathematica. Time used: 0.347 (sec). Leaf size: 230

ode=(1-x)*D[y[x],{x,2}]-4*x*D[y[x],x]+5*y[x]==Cos[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-4 x} \left (\operatorname {HypergeometricU}\left (\frac {21}{4},4,4 x-4\right ) \int _1^x\frac {e^{4 K[1]} \cos (K[1]) L_{-\frac {21}{4}}^3(4 K[1]-4)}{(K[1]-1) \left (21 \operatorname {HypergeometricU}\left (\frac {25}{4},5,4 K[1]-4\right ) L_{-\frac {21}{4}}^3(4 K[1]-4)-4 \operatorname {HypergeometricU}\left (\frac {21}{4},4,4 K[1]-4\right ) L_{-\frac {25}{4}}^4(4 K[1]-4)\right )}dK[1]+L_{-\frac {21}{4}}^3(4 x-4) \int _1^x\frac {e^{4 K[2]} \cos (K[2]) \operatorname {HypergeometricU}\left (\frac {21}{4},4,4 K[2]-4\right )}{(K[2]-1) \left (4 \operatorname {HypergeometricU}\left (\frac {21}{4},4,4 K[2]-4\right ) L_{-\frac {25}{4}}^4(4 K[2]-4)-21 \operatorname {HypergeometricU}\left (\frac {25}{4},5,4 K[2]-4\right ) L_{-\frac {21}{4}}^3(4 K[2]-4)\right )}dK[2]+c_1 \operatorname {HypergeometricU}\left (\frac {21}{4},4,4 x-4\right )+c_2 L_{-\frac {21}{4}}^3(4 x-4)\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*x*Derivative(y(x), x) + (1 - x)*Derivative(y(x), (x, 2)) + 5*y(x) - cos(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (-x*Derivative(y(x), (x, 2)) + 5*y(x) - cos(x) + Derivative(y(x), (x, 2)))/(4*x) cannot be solved by the factorable group method