5. Find the general solution of y"' + y'" - 6y' + 4y = 0 +

Q: (3) Show that the solution of the differential equation fip + y = -2r"y' is ´d.r r'y"(2r* + c) = 1.

A:

Q: 3) Find the solution of Initial Value Problem dy 2x-sin y dx 2x cos y ; y(4)=0

A:

Q: 2. Verify that the function y = Cjex + C2e2x is a solution of the differential equation y"– 3y' + 2y…

A: Given, the function y=C1ex+C2e2x is a solution of the differential equation…

Q: 10.Obtain the general solution of y(8x – 9y)dx + 2x(x – 3y)dy = 0

A: First we find tha integrating factor of given differential eq then we get exact differential eq.So,…

Q: 1. Determine the special solution of the Differential Equation y" – 2y – 3y = 64xe¬* with %3D…

A: To solve a differential equation  Find the characteristic equation of the homogenous equation…

Q: 1. Use the method of undetermined coefficients to find the solution of the initial value problem y"…

A:

Q: 4. Find the general solution of the given differential equations. (a) y" – y" – y + y = 0; %3D - (b)…

A: Given: The differential equation are: (a) y'''-y''-y'+y=0 (b) y'''-3y''+3y'-y=0 We have to find the…

Q: Find the general solution to the non-homogeneous differential equation. y" + 5y' + 6y = 3x2

A:

Q: Suppose we have the following system of linear differential equations: x' = 2x – 2y y = 2x – 3y. -…

A:

Q: Solve the initial-value problem y" + 4y" + 5y' + 2y = 10 cos t, y(0) = 0, y'(0) = 0, y"(0) = 3. %3!

A: The differential equation is y'''+4y''+5y'+2y=10 cos t , y0=0,y'0=0,y''0=3. The general solution of…

Q: 2. The differential equation (4x'y -6xy-2x-3dx + (2x*y – 2.x' kdy = 0 is exact because ƏM ON dy

A:

Q: Use Euler's method with step size 0.3 to compute the approximate y-values y(1.3) and y(1.6), of the…

A:

Q: 2. Find the solution of the given initial value problem using MUC: 2y(3) – y(2) – 2y(1) + y = 4x³ –…

A: Given: 2y3-y2-2y1+y=4x3-2xe-3x+5sin4x Initial conditions: y0=1, y'0=-2, y''0=3

Q: 3. Find the particular solution of the differen- tial equation: (x² +y² )dy=xydx, given that x=1…

A:

Q: 2. Obtain the general solution of x³y" + 3x2y' + x (+x) y = 0. Hint: The differential equation is…

A: Given: x3y''+3x2y'+x14+xy=0 To find: Bessel function.

Q: Show that y = C1e^2x + C2e^-x is a solution of the differential equation y"- y'-2y = 0. Also, find a…

A:

Q: 1) Use the Method of Undetermined Coefficients to find the General Solution to the Differential…

A: Given : Differential  equation is            y'' - 4y' - 12y = 2sin(t) To find: Find the general…

Q: 2. In the differential equation (x – 4y –9)dx+(4x+ y – 2)dy = 0 , the lines x- 4x + y- 2=0 intersect…

A:

Q: 5. Obtain the particular solution. y'"-2 y'+2 y=3e" cos 2x; when x 0, y=2,y'=3

A:

Q: Show that u(x, y) = xy is a solution of 2x- + y = 2x %3D дхду ду?

A:

Q: 16) The family of curves 4xy3 + 4y3 – y4 = C is the general solution of the differential equation:…

A: The given problem is to find the differential equation for which the given family of curves is the…

Q: 12. Use Euler's method with N 4 to numerically solve the initial value %3D problem y = 2y +t, 0<t<1,…

A: Given y′=2y+t,    given 0≤t≤1 y(0)=2, N =4 , we have to find Y4(1).  here h = (1-0)N=14=0.25 here…

Q: 3a. Verify that both yı(x) = 0 and y2(x) = (x – 2)ª %3D are solutions to the differential equation…

A: 3a.To verify that both  y1(x)=0 and y2(x)=(x-2)3 are the solutions of the differential…

Q: Find an explicit solution of the given initial-value problem. √₁-y² dx - √1-x² dy = 0, y(0) = -1/ 1-…

A: The given differential equation,1-y2dx-1-x2dy=0, y0=12

Q: Solve the separable initial value problem. 1. y' = In(x)(1+y²), y(1) = 1 → y= 2. y =…

A: Use the following formulas 1.∫xndx=xn+1n+1+c2.∫11+x2dx=tan-1x+c3,∫ln x dx=xln x-x+c

Q: 3. Find the general solution of the partial differential equation *** (x" + y" )z ; m, ne IR* . ây

A: Find the general solution of the partial differential equation: xm∂z∂x+yn∂z∂y=x+yn+mxm+ynz ,  m,n∈ℝ+

Q: Find the general solution for the system of differential equations. x' = -3x – 2y y' = 2x + y Use…

A: Consider the given differential equation.

Q: - Find the general solutions of the differential equations 6. x3 + 3y – xy' = 0 7. xy² + 3y² – x²y'…

A:

Q: Solve the problem := (1+ 4x)/y over the interval from from x = 0 to x = 1 using a step size of 0.25…

A:

Q: 4) Match the graph of the particular solution curve to the differential equation. (а) у" — Зу' — 4у…

A: First we calculate the general solution then match with given graphs.

Q: Solve the initial-value problem y" + 4y" + 5y' + 2y = 10 cos t, y(0) 0, y'(0) = 0, y"(0) = 3.

A: SOLUTION-

Q: satisfies

A:

Q: 2. Consider y+2-c y+1+cy, where e is a positive constant. For what values of e will the solution to…

A: Given yt+2-cyt+1+cyt

Q: Verify that y1 = x and y2 = xe" are solutions of the differential equation x²yll – x(x + 2)y! + (x +…

A:

Q: if y=x²sin(3inx) is a solution of a second order linear homogeneous differential equation, then the…

A: Given Differential Equation is 2nd order  Option (5) is Correct

Q: Solve the initial-value problem y" + 4y" + 5y' + 2y = 10 cos t, y(0) = 0, y'(0) = 0, y"(0) = 3.

A:

Q: Given that y, = 1, y2 = x2,y3 = e* are solutions of a third order differential equation (E). Then…

A:

Q: The differential equation of the form M (x, y) dx + N (x, y) dy = 0 that has been transformed to M1…

A:

Q: 4. Use the method of undetermined coefficients to find a particular solution to the system below.…

A:

Q: 6. Find the particular solution of 2xydx + (y² – x²)dy = 0 ;where y = 2 and x =

A:

Q: Show that xand x-³are solutions to the higher order differential equation x?y" + xy' – 9y = 0 with…

A:

Q: (b). By reversing the role of x and yY or otherwise, find the general solution to the differential…

A: Given:        2x-4y2dydx+y=0            2x-4y2dy+ydx=0    Equation in total differentials:…

Q: 15. The general solution of the differential equation xy^2 dy - dx = 0 is (3 Points) all of these 3…

A:

Q: (12) Show that the Initial Value Problem S lu(x)| = 1 rE (-1,1) u(x) = 0 r= -1,1 has no (classical)…

A:

Q: Obtain the differential equation belovw. y = Ce* + Cze-3x O y-3y +2y = 0 O y- 3y-2y 0 O y" +2y +3y =…

A: y=C1ex+C2e-3x

Q: 7.Obtain the particular solution of (1 – xy)-2dx + [y? + x²(1 – xy)-²]dy = 0 when x = 2, y = 1

A:

Q: Q.5. Find the general solution of the differential system 1 1 X' = 6.-1 X, %3D %3D -1 -2 -1

A: First we will find the eigenvalues and corresponding eigenvectors and then try to form the general…

Q: Find the particular solution of xy' - 4y = 0 ; initial condition y = 2 when x = 1.

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Q: 2. Obtain the general solution of: xy dx – (x² + 3y²) dy = 0

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Q: Solve the initial value problem: y/" + 12y" + 36y = 0, y(0) = 0, y'(0) = 1, y"(0) = –7. Hint: Higher…

A: