1. Solve the first-order linear differential equations. dy a) xx x+2y=1-¹, x > 0 dx b) = xy' + 3y= dy c) x +2y = 1- dx d) 2y' = ex/² + y e) xy' - y = 2x ln x sin x x2,X>0 x

Q: Which of the following equations are linear ordinary differential equations? 1. 7x² + yx = 0 2. 7x'…

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Q: The complementary function(C.F.) of the differential equation (D – 7)(D² + 7?)y = e7² is O (c2 Cos…

A: Solution: The objective is to find the complementary function of the given differential equation

Q: Solve the differential equation dy 2ay? + e + ( 2x y-4y 0. - dx a. 2æy? + e-2y2 = C O b. 2ay? + e +…

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Q: dy=(y + 9x) dx y + 9x = u

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Q: What is the general solution to the differential equation 2e* cot(y) dx – (4 + e*) csc²)dy = 0 ? (4…

A: Here, the given DE is: 2excot(y)dx-(4+ex)csc2(y)dy=0

Q: 1. Solve the first-order linear differential equations. a) x+2y= 1-1, x > 0 x

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Q/Solve the differential equation by seperable 1) dy=(y + 9x) dx 2) dx 3) dx - 1 1+ y² dy = 0 y + 9x…

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

A: We are given the solution as : y(t)=c1et+c2e2t-3tet+cos t-e-t2 ---(1)…

Q: 1. Find dy/dx a) y = In (2x² – 3x) %3D b) y = [e" dt ) d) y = In|sec(x)+ tan(x) e) y = 7std*) S)y =…

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Q: Solve the differential equation y"-3y'-4y 0 O y= e3* (c cos 2x + C2 sin 2x) cos 3x + c2 sin 3x) O y=…

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Q: Solve the exact differential equation (In y - y sin x-6e³x) dx + ( + cos x + 5 sec y tan y - 6y)dy =…

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Q: Q6. Determine the order, degree and state the linearity of the following differential equations: a)…

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Q: Let differential equation               ay'''+by''+cy'+dy=0 and solution of DE is spanned by ex,…

A: Let differential equation                  ay'''+by''+cy'+dy=0 and solution of DE is spanned byex,…

Q: Obtain the differential equation of a parabola with axis parallel to the x-axis. A 3(y")²-y'y"=0 B…

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Q: Make the Nonexact differential equation ry dx + (3y? + 2x2 – 20) dy =0 an exact differential…

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Q: Solve the Cauchy-Euler differential equation d'y dy +2x-20y xr + 2x +1 dx dx

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Q: Form the differential equation Por the curve y= 2sin (x + 3)

A: The order of the differential equation is the highest derivative present in the equation. The…

Q: Make the Nonexact differential equation xy dx + (3y2 + 2x2 – 20) dy = 0 to an exact differential…

A: The solution is given as

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

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Q: Find the general solution to differential equations 2 1) (-2xy) dx + (Siny-x²) dy 2) dy + 3xy dx = x…

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: Solve the first-order linear differential equations. a) x+2y= 1 - 1, x > 0 x

A: Note that : Since you have posted multiple questions, we will provide the solution only to the first…

Q: If the function y = a,(1+3x +x + +) is a solution of the differential equation Ay'-3y 0, then what…

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Q: 4. Explain the general behavior of solutions to differential equations of the form: a) df(t)/dt = +t…

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: Check whether the functions which satisfy the following differential equation are linearly…

A: Given differential equation x3d3ydx3+31-αx2d2ydx2+3α2+β2-3β+1xdydx-αα2+β2y=0 Given differential…

Q: / Solve three of the differential equations below: dy А. secx dx ev+sinx %3D B. (2y sinx - cos y) dx…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…