44.1.26 problem 28

Internal problem ID [6901]
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 : 28
Date solved : Monday, January 27, 2025 at 02:34:28 PM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 28

dsolve(2*x*diff(y(x),x)-y(x)=2*x*cos(x),y(x), singsol=all)
 

\[ y = \left (\sqrt {2}\, \sqrt {\pi }\, \operatorname {FresnelC}\left (\frac {\sqrt {2}\, \sqrt {x}}{\sqrt {\pi }}\right )+c_{1} \right ) \sqrt {x} \]

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 60

DSolve[2*x*D[y[x],x]-y[x]==2*x*Cos[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 \sqrt {x}-\frac {1}{2} i \left (\sqrt {-i x} \Gamma \left (\frac {1}{2},-i x\right )-\sqrt {i x} \Gamma \left (\frac {1}{2},i x\right )\right ) \]