44.1.8 problem 9

Internal problem ID [6883]
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 : 9
Date solved : Monday, January 27, 2025 at 02:33:29 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.072 (sec). Leaf size: 38

dsolve(sin(diff(y(x),x))=y(x)+x,y(x), singsol=all)
 

\begin{align*} y &= -\sin \left (1\right )-x \\ y &= \sin \left (-1+\operatorname {RootOf}\left (-x +\operatorname {Si}\left (\textit {\_Z} \right ) \sin \left (1\right )+\operatorname {Ci}\left (\textit {\_Z} \right ) \cos \left (1\right )+c_{1} \right )\right )-x \\ \end{align*}

✓ Solution by Mathematica

Time used: 16.078 (sec). Leaf size: 324

DSolve[Sin[D[y[x],x]]==y[x]+x,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{y(x)}\left (\frac {\cos (1) \sqrt {1-(x+K[1])^2} \cos (\arcsin (x+K[1])+1)}{2 (\arcsin (x+K[1])+1) (x+K[1]-1)}-\frac {\cos (1) \sqrt {1-(x+K[1])^2} \cos (\arcsin (x+K[1])+1)}{2 (\arcsin (x+K[1])+1) (x+K[1]+1)}+\frac {\arcsin (x+K[1]) \sqrt {1-(x+K[1])^2} \sin (1) \text {sinc}(\arcsin (x+K[1])+1)}{2 (\arcsin (x+K[1])+1) (x+K[1]-1)}+\frac {\sqrt {1-(x+K[1])^2} \sin (1) \text {sinc}(\arcsin (x+K[1])+1)}{2 (\arcsin (x+K[1])+1) (x+K[1]-1)}-\frac {\arcsin (x+K[1]) \sqrt {1-(x+K[1])^2} \sin (1) \text {sinc}(\arcsin (x+K[1])+1)}{2 (\arcsin (x+K[1])+1) (x+K[1]+1)}-\frac {\sqrt {1-(x+K[1])^2} \sin (1) \text {sinc}(\arcsin (x+K[1])+1)}{2 (\arcsin (x+K[1])+1) (x+K[1]+1)}+\frac {1}{\arcsin (x+K[1])+1}\right )dK[1]+\cos (1) \operatorname {CosIntegral}(\arcsin (x+y(x))+1)+\sin (1) \text {Si}(\arcsin (x+y(x))+1)-x=c_1,y(x)\right ] \]