The right hand side of the following first order problem is a linear function of x and y . Use the substitution v=x−y to solve the initial value problem. y′=sin^2(x−y), y(5)=5 We obtain the following separable equation in the variables x and v: ------------- Solving this equation and transforming back to the variables x and y we arrive at the implicit solution ----------- =x+C Finally we obtain the explicit solution of the initial value problem as y=----------
The right hand side of the following first order problem is a linear function of x and y . Use the substitution v=x−y to solve the initial value problem. y′=sin^2(x−y), y(5)=5 We obtain the following separable equation in the variables x and v: ------------- Solving this equation and transforming back to the variables x and y we arrive at the implicit solution ----------- =x+C Finally we obtain the explicit solution of the initial value problem as y=----------
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
In case an equation is in the form y′=f(ax+by+c), i.e., the RHS is a linear function of x and y. We will use the substitution v=ax+by+c to find an implicit general solution.
The right hand side of the following first order problem is a linear function of x and y . Use the substitution v=x−y to solve the initial value problem.
y′=sin^2(x−y), y(5)=5
We obtain the following separable equation in the variables x and v: -------------
Solving this equation and transforming back to the variables x and y we arrive at the implicit solution
----------- =x+C
Finally we obtain the explicit solution of the initial value problem as
y=----------
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y′=sin²(x−y), y(5)=5
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