Find general solution to Cauchy-Euler equation: (t^2)y''-2ty'-3y=t^2

Q: Use the 2 solutions Bernoulli's equation y' + -√√y=0 y x

A: The given differential equation y'+yx-y=0. We have to find the solution of the differential…

Q: solve y''-y'=xex using variation of parameter . Do not use any formula

A: using variation of parameter . First we find the solution for homogeneous equation. From that…

Q: Match the D.E. with a direction field: y' = t+y – 1, , y' = sin(t)sin(y), , y' = 2 – y, , y' = t(2 –…

A: NOTE: Horizontal axis is t-axis  .

Q: 4 -2) Q:Solve Y"= (;) Y.

A: We have to solve this differential equation.

Q: show that y=x2 is one of this equation solutions x2y''-2y=0

A:

Q: Solve y′  of (t^5+t)(t^3−4t+1)

A: ddtt5+tt3-4t+1Apply the Product Rule:  f·g'=f '·g+f·g'f=t5+t,…

Q: Solve using indeterminate coefficients y '' + 9y = x ^ (2) e ^ (3x) + 6

A:

Q: Solve: x^2y′′ + xy′ + x^2y = 0 where y(0) = 2

A:

Q: for

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Q: By Lagrange's formula, prove that y =y3-0-3(ys-y- 3) + 0-2 (y_ 3 -y_5).

A:

Q: Solve xy"- y' - 4x³y = 8x³sin(x²).

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Q: y + y = T+?" 1+ 12°

A: In this solution i got a critical integration which term i have conclude with a integral sign

Q: 2yy" = 1 + (y')² 2

A:

Q: solve given IVP showing details of your work,   y^iv  +3y'' -4y=0;  y(0)=3,…

A: solve given IVP showing details of your work,   y^iv  +3y'' -4y=0;  y(0)=3,…

Q: Solve the differeentail Equations for y"-2y'= 3x+9e^(3x)

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Q: Find the general solution of the Cauchy-Euler equation: X^3y’’’ - x^2y’’ + 2xy’ - 2y = x^3

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Q: Find a particular solution of the equation y4 -y3 - y" - y' - 2y = 8x^5:

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Q: when the parameter is eliminated from the equations x=t/2, y=t^3-4x+1 the resulting equation

A: The parametric equations are the group of equations with one or more variables having one common…

Q: 1 = felan(4x*). sec²(4x²)xde 2

A:

Q: Solve :     x²y"-2x(1+x)y'+2(1+x)y = x3

A: Given: The second order differential equation is x2y''-2xx+1y'+2x+1y=0

Q: Find the general solution of the DE: y’’’ - 4y’ = 32xe^2x - 24x^2

A:

Q: Solve:  y’’’ – 4y’’ + y’ + 6y = 0

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Q: reduce to linear form and solve the following equation y'+(1/2x)y=x/(y^3)  y(1)=2

A: The given differential equation is: y'+12xy=xy3  …1,   y1=2 This is Bernoulli's equation,so (1) can…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.