38.1.8 problem 9
Internal
problem
ID
[8169]
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
:
Tuesday, September 30, 2025 at 05:17:43 PM
CAS
classification
:
[[_homogeneous, `class C`], _dAlembert]
\begin{align*} \sin \left (y^{\prime }\right )&=y+x \end{align*}
✓ Maple. Time used: 0.031 (sec). Leaf size: 38
ode:=sin(diff(y(x),x)) = x+y(x);
dsolve(ode,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*}
✓ Mathematica. Time used: 0.106 (sec). Leaf size: 193
ode=Sin[D[y[x],x]]==y[x]+x;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\[
\text {Solve}\left [\int _1^x-\frac {\arcsin (K[1]+y(x))}{\arcsin (K[1]+y(x))+1}dK[1]+\int _1^{y(x)}-\frac {\arcsin (x+K[2]) \int _1^x\left (\frac {\arcsin (K[1]+K[2])}{(\arcsin (K[1]+K[2])+1)^2 \sqrt {1-(K[1]+K[2])^2}}-\frac {1}{(\arcsin (K[1]+K[2])+1) \sqrt {1-(K[1]+K[2])^2}}\right )dK[1]+\int _1^x\left (\frac {\arcsin (K[1]+K[2])}{(\arcsin (K[1]+K[2])+1)^2 \sqrt {1-(K[1]+K[2])^2}}-\frac {1}{(\arcsin (K[1]+K[2])+1) \sqrt {1-(K[1]+K[2])^2}}\right )dK[1]-1}{\arcsin (x+K[2])+1}dK[2]=c_1,y(x)\right ]
\]
✓ Sympy. Time used: 2.155 (sec). Leaf size: 80
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(-x - y(x) + sin(Derivative(y(x), x)),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
\left [ y{\left (x \right )} = C_{1} + x - \int \limits ^{- C_{2} - x} \frac {\operatorname {asin}{\left (r \right )}}{\operatorname {asin}{\left (r \right )} + 1 + \pi }\, dr - \pi \int \limits ^{- C_{2} - x} \frac {1}{\operatorname {asin}{\left (r \right )} + 1 + \pi }\, dr + \int \limits ^{- C_{2} - x} \frac {1}{\operatorname {asin}{\left (r \right )} + 1 + \pi }\, dr, \ y{\left (x \right )} = C_{1} + x - \int \limits ^{- C_{2} - x} \frac {\operatorname {asin}{\left (r \right )}}{\operatorname {asin}{\left (r \right )} - 1}\, dr - \int \limits ^{- C_{2} - x} \frac {1}{\operatorname {asin}{\left (r \right )} - 1}\, dr\right ]
\]