3. Determine a general solution to the Cauchy-Euler equation y (2) - 2y(z) = 3r-1, z>0. %3D

Q: 3. Find the general solution to y" – 3y' – 4y = 3x².

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Q: 4. (6 points) Using separation of variables, solve the differ- ential equation, (1+7)dy dx y Use C…

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Q: a) 2xy dx+(1+x²)dy=0 b) y'+(4/x)y=x* ------by exact method ---by linear method

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Q: Find the general solution of y""- 5y"- 6y'=0

A: The given differential equation y'''-5y''-6y'=0

Q: 1. Solve the equation y2 + 6x = y(3y – 2x)y'

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Q: ) Verify that y=e-2x is a solution of equation x(y")3+ (y')4 – y = 0

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Q: Find the solution of the Euler-Cauchy equation x²y" + 0.6xy' + 16.04y = 0.

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Q: 1. Find a general solution of the first order equation: y'= 3x²y².

A: The given first order differential equation is solved by method of separation of variable.

Q: y" + 7y' + 10y = -1lte".

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Q: 5) Form a DE by eliminating the arbitrary constants from the equation y = asin(4x + 1).

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Q: 3. Solve (2xy – y² + y)dx + (3x² – 4xy + 3x)dy = 0. (Non Exact) 4. Solve the following FOLDE: (2у +…

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Q: 2 Find the general Solution of yty = 2xcosx -CosX %3D

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Q: Find the solution. (dy/dx) + xy = xy³ A x = (ce-²-1) By = (ce²+1) 7² y = (ce x²-1) x = (ce)² + 1) ²…

A: We have given a differential equation ,  dydx + xy = xy3 Multiply throughout by dx ,  dy + xy dx =…

Q: 5. Exact Diffe re ntial Equation: x(3xy – 4y' +6}dx+(x' – 6x² y² -1dy =0

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Q: Verify (do not solve) that y(x) = 3x + 2x-1/3 is a solution to 3xy' + y = 12x.

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Q: Find the complementary solution of the equation y" - 5y" +7y' – 3y = 0

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Q: 7. Linear Equation of Order 1: Solve the equation 2 (y – 4x²) dx + xdy = 0

A: The given equation is first order differential equations and can be written is in the firm of dy/dx…

Q: 1. Find the general solution of У"-Зу'— 4х? —2у

A: See the attachment

Q: Solve the give differnetial equation by undetermined coefficients y''' - y'' -16y' + 16y = 5 - ex +…

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Q: Find the value of a, if y(x) = = (C₁+C₂ In x) is solution of the Cauchy Euler equation a²x²y" + a(a…

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Q: (2xy³ + 1) dx + (3x³y² - +) dy=0 y(5)=n Determine the interval ON which the solution exists.

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Q: Find General Solution of y" + y" = 0.

A: Given the differential equation is y"' + y" = 0. Here the auxiliary equation is m3 + m2  = 0