6. Given that y = 0 when x = 1, show that the solution of the differential dy equation 2xy- - = y² + 4 is y = 4x – 4. dx

Q: 2. Show that y = e-6t satisfies the differential equation y" – y – 42y = 0.

A: We have to verify that y''-y'-42y=0 when y=e-6t. We know that d2ydt2=y''dydt=y'de-atdt=-ae-at So…

Q: 8. The differential equation (2x-xy-2y+3}dx-(x*y+2xkty = 0 is exact because ÔM ON

A:

Q: What is a particular solution to the differential equation 2y dx – 3x dy = 0 when x = 1 and y = 1?

A:

Q: 8. Use a substitution to solve the homogeneous 1st order differential equation (x – y)dx + x dy = 0

A:

Q: Find the equation which satisfies the separable differential equation dy – 15x dx with the initial…

A: Given dydx=-15xy    y(1)=-5To find solution:

Q: Is (1+ex/y)dx + ex/y(1-x/y)dy = 0, a exact differential equation? If yes then, find the value of y.

A: Exact differential equation- A differential equation of the type Mdx+Ndy=0 is said to be exact if,…

Q: By using variation of parameters, what is a possible value for u' for the differential equation y' +…

A:

Q: Find the particular solution to the differential equation. 4y2 dx = 3x2 dy when x = 4, y = -1 %3D

A:

Q: What is the particular solution to the differential equation dx 1 + y = 2e-* with y = 1, dy -1 when…

A:

Q: Find the particular solution of the differential equation with the initial condition given below.…

A:

Q: 2x-y? xy? 3- ()dr – ()dy = 0 is exact differential equation. True False o o

A:

Q: What is the integrating factor to (2y2 + 3xy – 2y +6x) dx + x (x + 2y – 1) dy = 0, to make it an…

A:

Q: y(x²y² – 1)dx + x(x²y² + 1)dy = 0

A:

Q: 5. Verify that y(x) = Vx+C is a solution of the differential dy dx 1 for every constant C. equation…

A: The differential equation is given as dydx=12y2ydy=1dx

Q: dyr+y+3 e non-homogeneous differential equation can be solved by putting %3D dz 5z + 5y + 4 Ov= 3z -…

A:

Q: Consider the differential equation x²y " – xy ' + y = 0. Given that y(1) = 2 and y '(1) = 3,…

A:

Q: x - yArctan | dx + xArctan ) dy = 0 %3D

A:

Q: Obtain the general solution for the following differential equation using Separation of Variables…

A: Using method of seperation of variables

Q: What is the particular solution to the differential equation dy/dx=xy2 with initial condition y(2) =…

A: To find the particular solution

Q: Show that xy = ae" +be* +x is a solution of the differential equation. d'y +2- -x+x-2=0. X dx

A: If we differentiate   the given  solution equation two times  and  get  the given differential…

Q: SOLVE FOR EXACT DE DIFFERENTIAL EQUATION хdy — ydx 4. | = x³ dx y2

A: Given that: xdy-ydxy2=x3dx

Q: Find the solution to the second order differential equation y'' = T COS(TX) with initial conditions…

A:

Q: Solve the given differential equation by separation of variables. (ex + 1)²e-y dx + (ex + 1)4e¯* dy…

A: Given : ey+12e-ydx +ex+14e-xdy=0 To Find : Solution of given differential equation

Q: What is the general solution to the differential equation dydx=(x−1)/(3y^2) for y>0y>0

A:

Q: 2. What should be A for the exact differential equation of ry + A , 2Ay – 1 dr+ y? Moreover evaluate…

A:

Q: 5. With the substitution cosy == differential equations sin y dy – cosy(1 – x cosy)dx=0 reduced to a…

A: Substitute  cosy=1tNow differentiate it with respect to t,-sinydy=-1t2dtsinydy=1t2dt

Q: What is the particular solution to the differential equation [x+(1+x)y] = 12 with y = 0 and =0 when…

A:

Q: What is the integrating factor of the differential equation (5xy + 4y² + 1) dx + (x² + 2xy) dy = 0?…

A:

Q: By using variation of parameters, what is a possible value for u'1 for the differential equation y''…

A:

Q: 2. Find the particular solution for the dy differential equation dx = 2xy and y = 3 when x = 0

A: We will find the particular solution of the differential equation , dy/ dx  = 2xy   .

Q: 3. Given that y = 1 when x=-1, find particular solution to differential equation dx dy – 3x²y² =…

A:

Q: Without using an Integrating Factor, determine the particular solution of the given differential…

A:

Q: 9. The differential equation (3y cosx+4xe" + 2x'e' dx + 3(sin x +1)dy=0 is exact because aN

A:

Q: 4. Use separation of variables to find the general solution of the differential equation. dy = 5t+1…

A:

Q: 8 Find the general solution of the differential equation: xy' + y: X Use lower case c for constant…

A: Given : xy'+y=8x+9x Following formulas are used- ∫1xdx=lnx∫xndx=xn+1  n+1

Q: 4. Given that x=0 when y = 8, show that the general solution of the differential dy equation (x +4)…

A:

Q: 4. Find the general solution to the differential equation y" + 4y = cos 2x (where y' = ) dx

A: The general solution of a higher-order linear non-homogeneous differential equation is the sum of…

Q: Determine the particular solution to the differential equation dx dy = xy + x which satisfies y = 3…

A:

Q: Show that (y^2-1)^2=Ax is the general solution of the differential equation 4xy dy/dx =-1+y^2.

A:

Q: What is the General and Particular solution of the Differential Equation 2x(y+1)dx-ydy=0? Where x=0…

A:

Q: Q3: if y'-f(y/x) where v-y/x Find a solution to the differential equation 2xyy'-y2+x2 =0 ?

A: Given

Q: Consider the differential equation y = x+ y. Use Euler's method with Ax = 0.1 to estimate y when x =…

A: Let fx,y=x+y. Substitute 0 for n, 0.1 for h, -1 for x0 and 0 for y0 in the Euler's formula…

Q: 20.Find the particular solution of the differential equation x +1) = x3 – 2y, given x = 1 dx when y…

A: We have to find general solution of given differential equation with initial condition.

Q: 3. Verify by direct substation that y = > Cn x", is a solution of this linear differential equation…

A:

Q: 45. The particular solution of the differential equation x^2 dx - (y+1) dy = 0 if at x=1, y3D0 is_

A: Given differential equation is x²dx - (y+1)dy = 0

Q: Obtain the general solution of the given differential equation up to the form free from ln function.…

A:

Q: Show that given differential equation is not exact and hence find its general solution (x³ + y°)dx –…

A:

Q: xydx + 2(x2 +2y)dy=D0; when x= 0, y= 1

A:

Q: 4. Use separation of variables to find the general solution of the differential equation. dy = 5t*…

A:

Q: What is the general solution to the differential equation (tan x)dy – (4y In y – y tan³x)sec²x dx =…

A: We will convert given differential equation into linear differential equation by appropriate…

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.