(D² + 4) y = tan 2x

Q: Solve the differential equation dx/dt = 1 - t +x -tx for x(-1) = -2

A: Given : dxdt = 1 - t + x  - txx-1 = -2

Q: find the general solution of the first-order linear differential equation. y' + (tan x)y = cos x

A:

Q: Show that the differential equation  (2xy3 - 3y2 + 2xy2)dx + (3x2y2 - 6xy + 2x2y)dy = 0 is exact and…

A: To show that the differential equation  2xy3-3y2+2xy2dx+3x2y2-6xy+2x2ydy=0 is exact and to find its…

Q: 1. Solve the linear differential equation of y' – 2xy = = X. swer:

A:

Q: The standard form of the first order linear differential equation xdy+(2xy – 3y-4x“ )dx= 0 is_

A:

Q: Find the integrating factor of the non-exact differential equation: dy= (e2x+y-1) dx

A: Given differential equation is dy=e2x+y-1dx which can also be written as e2x+y-1dx-dy=0 Comparing…

Q: Find the differential equation of the cubics : cy^2= x^2 ( x - a ) with a held fixed.

A: Here c is arbitrary constant and a  is fixed. So we have to find a differential equation which does…

Q: y = Ce * + C2e 2x + C3e * + e 2x

A: y=c1e-x+c2e-2x+c3e-x+e2xy=c1+c3e-x+c2e-2x+e2x Here, complimentary solution is  y=c1+c3e-x+c2e-2x…

Q: The indicial equation for the differential equation 2xy" + y + xy = 0 is 2c² - 1 = 0. True False

A:

Q: Find the general solution for the first-order differential equation. dy dx 16x

A: We have to find general solutions of given equation.

Q: Solve the Cauchy-Euler differential equation x -2x+2y = x dx dx

A:

Q: b Show that y = e' sinx %3D satisfies the differential equation (1 - x²)y" – xy' - y = 0. |

A:

Q: What is the standard form of this linear differential equation in one variable. Y + 1)dx + (4x – y)…

A:

Q: 6. (D² + 1) y = x cos x

A:

Q: Is x = 0 an ordinary point of the differential equation y″+5xy′+√xy=0 ?

A: We have to check

Q: Determine if the given differential equation is homogenous. (x³y³+1)dx + x⁴y²dy =0

A: Given differential equation (x³y³+1)dx + x⁴y²dy =0 Now we will check whether the given differential…

Q: find the general solution of the first-order linear differential equation. y' − (ln x)y = xx

A:

Q: e. Cxy +C'x + 9 = 0

A: Cxy+C2x+9=0

Q: What is the general solution to the differential equation (2xy – tan(y))dx + (x² – xsec?y)dy = 0? |

A: First we have to show that the differential equation is exact. Then we find the general solution of…

Q: Obtain the differential equation associated with the primitive y = Ae3x + Be2x + Ce*.

A: Given differential equation is we have to obtain the differential equation associated with the…

Q: Find the differential equation of dy/dx = x+y/x-y

A:

Q: Find the general solution of the first-order linear differential equation y′ + 2xy = 10x for x >…

A: Given y'+2xy=10x

Q: Find the differential equation of the family of -2x y = A1eª + A, e 2a

A:

Q: Solve using the non-exact linear differential equation  [ytan(x)(cos(2x))-1]dx+csc(2x)dy=0 when…

A:

Q: у" - 2у' + у %3D et + Зех 1+x2

A:

Q: Find the integrating factor of the non-exact differential equation : (3x²y+6xy+y³) dx+3(x²+y²) dy=0

A: Given a differential equation, 3x2y+6xy+y3dx+3x2+y2dy=0. To find the integrating factor of the given…

Q: The Bernoulli's form of the differential equation xdy - [y + xy³ (1 + ln x)]dx = 0 is

A:

Q: Solve the non-homogenous differential equation below dy 2y + x - 3 dx y + 2x – 3

A:

Q: What is the general solution of the differential equation; y’ = 2x cos (x^2)

A: solution:-y'=2x cosx2solving the differential equation we getdydx=2x cosx2y=∫2x cosx2 dxlet x2=t2x…

Q: y = Ax² + Be*

A:

Q: 2) x – 1 = - 2e-y

A:

Q: Consider the differential equation 2²y" – x(x + 2)y + (x + 2)y = 0, x > 0 - 3.

A: Given: x2y''-xx+2y'+x+2y=0, x>0   To find: A second solution y2x using the solution y1x To show:…

Q: (メyーx+24 -2) dx- (x+ 4x) 0

A:

Q: Find the I.F of this nonexact differential equation dy/dx=1/(2xy)

A: Please see the answer below.

Q: Find the solution of the Linear Homogenous Differential Equation Cofficients. D²(D + 2)*y = 0 =D(

A:

Q: The Bernoulli's form of the differential equation x³ydx +(3x² - y³)dy=0 is

A: To determine the Bernoulli's form of the differential equation x3y dx+3x4-y3 dx=0.

Q: Find the general solution to the non-homogeneous differential equation. y" - 3y' = sin(3x)

A:

Q: B2. Find the general solution of the linear differential equation. (tan-ly-x) (1+y²) dx dy

A: Concept Used: A first order differential equation is said to be linear differential equation if it…

Q: Determine the form of a particular solution of the differential equation y" + 9y = e*cos3x + x² +…

A:

Q: y = C1e2" sen(x)+ C2e²" cos(x) +x² + C3x + C4.

A:

Q: The solution for the differential equation dy dx tan-¹x 1 1+x² (et - y is

A:

Q: Find the linear, nonhomogeneous differential equation with constant coefficients whose solution is y…

A: We have to find homogeneous part of the differential equation first.

Q: Find the homogeneous linear differential equation whose solution is y=-e^(3x/2)-4x sin⁡2x.

A:

Q: Find the Differential equation by eliminating the arbitrary constant x2 - y2 = a2

A:

Q: (D² + 1) y = x cos x

A:

Q: Consider a differential equation y' = xy + xe -x

A: To solve a differential equation:

Q: The differential equation (2x' - xy - 2y+3 dx- (x²y+2xdy = 0 is exact because OM ON

A: