x+3y -4 3. Find the general solution of y' = 5-x-4y

Q: Find the general solution valid near x=0 (x2 + 4) y" + 2xy' -12y = 0

A: We have to solve given problem:

Q: 8x²y" + 10xy' – (1+ x)y = 0

A:

Q: Find the solution of 2y-y² sec²(xy²) + (2x − 2xysec² (xy²))y' = 0 given y(1) = 2.

A:

Q: Find the general solution of the DE: y"+y' + 2y = 0

A:

Q: Find the general solution of: y(x°+x*)dx - x(x³+ y-)dy = 0

A:

Q: 4. xydx + (y √ x² + y²-x²) dy=0

A:

Q: a) Solve y' = 3x² + y, y(0) = 4 by choosing step length 0.1 for y(0.2) by Euler's improved method

A:

Q: Obtain the general solution valid near the origin: x(x − 2)y" + 2(x − 1)y' − 2y = 0

A:

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

A:

Q: find the general solution of the given equation. 3y'' - y' = 0

A:

Q: particular

A: We find particular solution.

Q: ) Obtain the general solution of y" + 2y + y = e² In r

A: In this question, the concept of the differential equation is applied. Differential Equation A…

Q: find general solution. dr/dt= -2tr,         r(0)=ro

A:

Q: Find the general solution of y’ + (1/3)y = exy4

A: We have to find the general solution of the differential equation y'+13y=exy4 .

Q: Find the general solution for the homogenous equation of y′′ − y′ − y = 0.

A:

Q: Obtain the particular solution of (3x2 - 2y2)y' = 2xy; x =0, y=-1.

A: We have to solve

Q: (a) Solve y" + xy + (2r – 1)y = 0, %3D near z = -1, if y(-1) = 2; y'(-1) = -2.

A:

Q: 6. Find a general solution to the third order equation y" + y" + 3y – 5y = 0.

A:

Q: Obtain the general solution. (xy + x) dx = 2 2 y + x + y¯ +

A: The given differential equation is…

Q: Obtain the general solution valid near the origin: 8x^2y" + 10xy' − (1 + x)y = 0

A:

Q: Give a particular solution for y" – 2y' + y = 1+x2

A: Given that a differential equations - y" -2y' +y = ex/1+x2.   We know that integration of 1/(a2 +x2)…

Q: Find a particular solution for: y" - 3y' + 2y = te*

A:

Q: Q1: Solve the second order linear homogenous equation: y" – 2ky' + 4y = 0 k > 2 -

A: According to our guideline we can only answer first question and rest can be reposted.

Q: 2. (D² - 3D + 2)y=1+x

A: The given differential equation is;  (D2-3D+2)y=1/(1+e-x).

Q: 4. Find for the particular solution of y' = x3 – 2xy when x = 1, y = 2 x2 а у 2e + 2 - ex2 b. y =+…

A: The given differential equation is:y'=x3-2xywhich can be written asdydx+2xy=x3which is a first order…

Q: dy 3. Solve dx = -8xy² +4x(4x+1)y-(8x' +4x² -1) by knowing u = x is a solution.

A: Given differential equation is dydx=-8xy2+4x4x+1y-8x3+4x2-1             …(1) y=x is a solution of…

Q: xy' – y = 2x lnx

A:

Q: y""+y" = 3x² + sin x - 2 cos x

A:

Q: Use undetermined coefficients to find the particular solution to y'' – y' – by = 2e-2 Y(t) =

A:

Q: ) Give a particular solution for y" – 2y' + y = 1+x² *

A:

Q: Obtain the general and particular solution 4. xydx + (x² + y²)dy = 0

A: The given problem is solved below in detail.

Q: 3. Obtain the general solution of: (x – y)(4x + y) dx + x(5x – y) dy = 0

A:

Q: *+ 2y = te-2t, y(1) = 0 2. Solve the IVP: dt

A:

Q: ) Find the general solution of the DE y = (2+y')x+ (y')².

A:

Q: Solve for the general solution xydx - (x² +2y² ) dy = 0 x² = 4y° In(2 ) xy = 4y° In() Option 1…

A:

Q: Find the solution of y-x =0 using separable variable method. dx

A:

Q: Yp = Find a particular solution to y" + 5y' + 4y = - 19te³t.

A: Introduction: The differential equation has a particular solution, which is a singular solution of…

Q: Solve the system of differential equations x' = 18x + 3y y' = – 70x – 11y - - x(0) = 11, y(0) = – 52…

A: The given system of differential equations are…

Q: Xyz = 0 12. Solve: {x+ 2z = 1 2y-z 4

A:

Q: Find the general solution of y" + 2y=ex +2.

A: The Auxiliary equation is D2+2=0 solve for D Therefore  D=±-2=±2i Therefore the solution is…

Q: Use variation of parameters to find a particular solution of y'' - Y = 4e-x 1-e-2x Yp (x) =

A: Solution of the differential equation, By using the method of Variation of perameters

Q: Use variation of parameters to obtain the general solution. y''+4y = 4 sec2x

A: The given differential equation is; y"+4y=4sec2x.

Q: X-2y+3z=11 4x+2y-3z=4 3x+3y-z=4 Solve by  Gaussian elimination

A:

Q: Use variation of parameters to find the general solution of y" – 2y' + 5y = e'.

A:

Q: Obtain the general solution valid near the origin: 8x?y" +10xy' -(1+x)y=0

A: Power series solution of the differential equation

Q: xyz = 0) Solve: {x+2z = 1 (2y– z = 4

A: xyz=0  x+2z=1  2y-z=4

Q: 2. Solve the IVP: *+ 2y = te-2", y(1) = 0 dt

A: