Question

Using Mathematica code, use DSolve to find the solves to the following differential equations : a.xUsing Mathematica code, use DSolve to find the solves to the following differential equations:

a. x²y′′ + 3xy′ − 4y = 0
b. x²y′′ − 3xy′ − 4y = 0
c. 2x²y′′ + 7xy′ + 5y = 0
d. 2x³y′′′ + 9x^2y′′ − 10xy′ − 8y = 0

Answer 1

To solve the given differential equations using Mathematica code, we can use the DSolve function. Each equation is provided along with the corresponding code to find the solutions.

Step-by-step explanation:

To solve the differential equations using Mathematica code, we can use the DSolve function. Here are the solutions for each given equation:

a. x²y′′ + 3xy′ - 4y = 0:

D Solve[x^2 y''[x] + 3 x y'[x] - 4 y[x] == 0, y[x], x]

b. x²y′′ - 3xy′ - 4y = 0:

D Solve[x^2 y''[x] - 3 x y'[x] - 4 y[x] == 0, y[x], x]

c. 2x²y′′ + 7xy′ + 5y = 0:

D Solve[2 x^2 y''[x] + 7 x y'[x] + 5 y[x] == 0, y[x], x]

d. 2x³y′′′ + 9x^2y′′ - 10xy′ - 8y = 0:

D Solve[2 x^3 y'''[x] + 9 x^2 y''[x] - 10 x y'[x] - 8 y[x] == 0, y[x], x]