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(1 point) Write the equation in the form y'= f(y/z) then use the substitution y mu to find an implicit general solution.
Posted: Wed Jul 06, 2022 11:50 am
by answerhappygod
- 1 Point Write The Equation In The Form Y F Y Z Then Use The Substitution Y Mu To Find An Implicit General Solution 1 (33.4 KiB) Viewed 10 times
(1 point) Write the equation in the form y'= f(y/z) then use the substitution y mu to find an implicit general solution. Then solve the initial value problem. 3y² + 2x² xy The resulting differential equation in z and u can be written as zu y du da y(1) = 3 x 2/x Separating variables we arrive at sqrt(x^4-1) Separating variables and and simplifying the solution can be written in the form u²+1=Cf(x) where C is an arbitrary constant and xsqrt(Cx which is separable. Transforming back into the variables a and y and using the initial condition to find C we find the explicit solution of the initial value problem is / xsqrt(10x^4-1)