Mathematics, 26.02.2020 05:43 tonya3498
In case an equation is in the form y′=f(ax+by+c)y′=f(ax+by+c), i. e., the RHS is a linear function of xx and yy. We will use the substitution v=ax+by+cv=ax+by+c to find an implicit general solution. The right hand side of the following first order problem.
The right hand side Of the following first order problem
y' = (5x — 3y+ 1)^1/2 + 5/3, y(0)=0
is a function Of a linear combination Of z and y, i. e y'= f(ax+by+c). To solve this problem use the substitution v= ax + by +c which transforms the equation into a separable equation.
We obtain the following separable equation in the variables Z and V:
a. Solving this equation an implicit general solution in terms 0f x, v can be written in the form:
x+ = C
Transforming back to the variables Z and y the above equation becomes
x+= C
Next using the initial condition y(0)= 0 we find C :
Then, after a little algebra, we can write the unique explicit solution of the initial value problem as:
y=
Answers: 1
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In case an equation is in the form y′=f(ax+by+c)y′=f(ax+by+c), i. e., the RHS is a linear function o...
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