Second order linear diff. equation

find y as a function of t if 4y'' +30y = 0 y(0)=5 y'(0)=7

Second order linear diff. equation

find y as function of t if 64y'' + 64y' +18y = 0 y(0)=4 y'(0)=4 in terms of sine and cosine

Differential Equations

Find y as a function of x if: (x^2)(y'') + 15xy'+49y = 0 y(1) = -4 y'(1) = -3

Second order ODE

Find y as a function of x if: (x^2)(y'') - 5xy' -16y = 0 y(1)=2 y'(1)= 9

Second order ODE

Find y as a function of t if 16y'' - 88y' +121y = 0 y(0) = 4 y'(0) = 9

Second order ODE

find y as a function of t if 64y'' + 32y' +4y = 0 y(5)=6 y'(5) = 5

Differential Equations

For each of the following ordinairy differential equations, indicate its order, whether it is linear or nonlinear, and whether it is autonomous or non-autonomous. a) df/dx +f^2=0 (See attachment for all questions)

Solve the ODE (Integrate)

Find the explicit solution to the ODE 2yy'=(1+y^2) subject to y(0)=4. What is the solution if y(0)=-4? *(Please see attachment for proper citation of symbols and numbers)

Ode (Boundary Condition, Implicit and Explicit Solutions)

Consider the ODE y' = y2/x subject to the boundary condition y(1)=1. Find an implicit solution of the form H(x,y) = constant, then find an explicit solution of the form y=y(x). What is the largest x-interval on which the solution is defined? *(Please see attachment for proper citation of symbols and numbers)

Solving an ODE

Find all solutions to the ODE yy'= (1-y^2) sin x. (When dividing by 1-y^2, be careful that you don't lose any solutions). NOTE: y2 = y squared Please see attached file for full problem description.