9. Find the general solution of (2ху — у2 +у) dx+ (3x - 4xy + 3x) фу — 0 А. ху"(x - у + 1) %3D с В. х'у(x - у + 1) %3D с С. ху"(x - у + 1) %3D с D. x'y?(x - у + 1) %3D С

Q: The separable equation dy/dx=xy2 admits a constant solution equal to (x)=0. Is it True or False?

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Q: Solve system of linear DEs  dx/dt+dy/dt+2y+6y=2e^t 2dx/dt+3dy/dt+3x+8y=-1

A: To solve dxdt+dydt+2x+6y=2et2dxdt+3dydt+3x+8y=-1

Q: Show that the equation x2 + y2 = 2003 has no solutions in theintegers.

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Q: 1. Find the general solution of: du dx _ _ y + xy² + x³ x+x²y+y² dy

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Q: 3. Solve the initial-value problem: 2 dy = 2xy + 3y y(1) = dx 1

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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: Example 2: Find the particular solution of (x – y)dx + (3x+y)dy = 0 when x = 2 & y = -1.

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Q: 3. General solution of (ylny - e-xy)dx + ( + xlny) dy = = 0

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Q: what value of n can be used to transform the Bernoulli equation y'+p(x)y=q(x)y^n into an equation of…

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Q: Find a particular solution to y" + 5y' + 6y = lte".

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Q: (x-2)²(x³-4) y = Vx2+1 dy If then equals to : dx O y [2/(x-2)+(3x^2)/(x^3-4)-2x/(3x^2+3)] O…

A: The formulas which are used to solve the above problem are stated with the solution.

Q: I. Find the general solution of the following: 1. dx dy -2x + 3x² dy 2. dx = 3e-2x 3. (x² + 5)dx –…

A: Differential equation problem....

Q: Find the general solution of (xy + 4x)y = 5y² + 4xy². a) Oy + 12y- = -5 In |x| – 16x + C b) Oy - 4y-…

A: First order non linear ordinary differential equation.

Q: Verify that y=2 cos(3x) is a solution to the initial value problem: y"+9y=0, y(0)= 2

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Q: 3. Show that the equation (6xy – y*)dr + (4y + 32² – 3ry²)dy = 0 %3D is exact. Hence solve the…

A: Given that  The differential equation is  To solve the differential equation with intial condition

Q: Suppose we are given y₁) and y2(x) (with y₁ ‡ y2), which are two different solutions of a…

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Q: Solve the initial value problem. 2x* - х - 4 2 dy X dx (x+1)(у+1) y(1) = 3

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Q: こU)+2vl)-u= 0

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Q: the general solution to the DE xy3 dx +ex^2 dy=0 is

A: Given : xy3dx+ex2dy = 0

Q: Find general solution of (4x + 6y)dx + (8x + 12y − 6)dy = 0 (DE WITH COEFFICIENTS LINEAR IN 2…

A: We have to solve given problem:

Q: 3. Solve the Bernoulli DE: 5 dy - 5y : dx | - 2

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Q: 2. Give the general solution of xy'dy = (x³ +y³)dx in explicit form.

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Q: 4. Solve the initial value problem- dx dy 3x? +4x + 2 2(у-1) y(0) = 2 and state the interval in…

A: Given differential equation is : dydx=3x2+4x+22y-1 To solve the given differential equation.

Q: Solve the initial value problem: (4y + 2x – 5)dx + (6y + 4x – 1)dy = 0, y(-1) = 3 Clearly label your…

A: Initial Value Problem: In multivariable calculus, an initial value problem is anordinary…

Q: 1. Solve the initial value problem dx - x* (1+ y) = 0, y(0) = 5.

A: Explanation: Given that,  dydx-x6(1+y)=0, y(0) Now,  dydx=x6(1+y)1(1+y)dy=x6dx

Q: Find the general solution of the Cauchy-Euler equation: X^3y’’’ - x^2y’’ + 2xy’ - 2y = x^3

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Q: Solve the initial-value problem d²y 4- - 4 - 3y = 0, y(0) = 1, y'(0) = 5. dx2 dy dx

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Q: 1. (a) Show that (x) x² is an explicit solution to dy X- = 2y dx on the interval (-∞, ∞). (b) Show…

A: An explicit solution is any solution that is given in the form y=y(x)

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: Find the solution of the initial value problem dy 2 - - 4y + 0, y(1) = 2 dx

A: Given differential equation is −xdydx−4y+2x2=0......1 and y1=2. We have to find the solution of the…

Q: the solution to the IVP(x2+y2)dy/dx+xy=0 with y(0)=2 is

A: Given DE is x2+y2dydx+xy=0  and y(0)=2 find the solution of the DE

Q: 4. Find the solution of (x²+6y²)dx – 4xydy=0 when x=1, y=1. Use Substitution Method.

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Q: #14

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Q: Solve dy 4y dx x(y - 3) By using the method of separable variables. 1- y - 3 Iny = 4 ln x + C Option…

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Q: Solve the Initial Value Problem. (1 – 3t)– dy - у %3D 0, у(2) %3D —4 dt

A: The given differential equation is 1-3tdydt-y=0...(1) The initial condition is y2=-4.

Q: Find the general solution of the Cauchy-Euler equation: x²y" – 3xy + y = x°, x>0.

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Q: Find the general solution of DE:  1. (x-4y-3)dx - (x-6y-5) dy = 0

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Q: How do I solve dx/dt+2x=3 with a particular solution of xp=3/2?

A: To find the general solution of the equation, given the particular solution

Q: 7. Solve the following Cauchy-Euler equation d’y dx² dy +5x- +3y = In x. dx

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Q: 2) .. Use separation of variables to find the general solution.   dy dt − 12t3e−y = 0.

A: Answer: The solution is as given below:

Q: Solve the equation. 3x²y¯1 )dx + (2 – 4x°y¯2)dy = 0 :- An implicit solution in the form F(x,y) = C…

A: We have given 3x2y-1dx+2-4x3y-2dy=0 If we take M=3x2y-1 and N=2-4x3y-2 Then, ∂M∂y=-3x2y-2 and…

Q: 1. Find the particular solution of the DE: y' = (x^3) + e^(10x) + 7 if y = 20.1 when x - 0. You may…

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Q: 2. Give the general solution of xy dy = (x³ + y³)dx in explicit form.

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Q: 1. Find that solution of y' = 2(2x-y) which passes through the point (0, 1). Use Linear Equation of…

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Q: (1 – xy)-2 dx + [y² + x²(1 – xy)¯2] dy = 0; when x = 4, y = 1.

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Q: Find the general solution of the given DE (x-3y-1)dx-(x-3y+5)dy%3D0.

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Q: 1. Find the general solution of: dx dy _y+xy²+x² x+x²y+y³

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Q: Solve the general solution of the given DE * dy = (-5x + y)² – 4 dx 3 (1+ ce6x ) 3 (1 – ce6*) y = 5x…

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