dydx=dy1dx+cd(y1−y2)dx=dy1dx+c(dy1dx−dy2dx) This simplifies to: dydx=(1+c)dy1dx−cdy2dx Step 5: Substitute into the original equationSubstituting y into the original differential equation: dydx+P(x)y=Q(x) Substituting y: (1+c)dy1dx−cdy2dx+P(x)(y1+c(y1−y2))=Q(...
Verify that the following is an exact differential equation and then solve the equation: \left [ 2xy cos(x^2 y) + 2e^{2x} \right ] dx + \left [ x^2 cos(x^2 y) - 6y^2 \right ] dy = 0 Verify that the following is an exac...
Find a function F(x,y) whose level curves are solutions to the differential equation (x2+3xy)dx+xdy=0. F(x,y)= First order differential equation: The equation of is in the form of M(x,y)dx+N(x,y)dy=0. First check the equation ...
Answer Step by step video & image solution for Solutions of the differential equation (1-x^2)(dy)/(dx)+xy=ax where ainR is by Maths experts to help you in doubts & scoring excellent marks in Class 12 exams.Updated on:21/07/2023Class...
The simplest method of finding the solutions of a differential equation is to segregate the variable and to integrate the functions distinctly to obtain the general solution of the differential equation. As an example the differential equation dy/dx = 2x/(3y -1) is segregated such that the expr...
We introduce the notion of almost continuability of the solution of the differential equation of first order dy/dx = f(x, y) to the whole real axis. We give a criterion for the almost continuability of solutions for the case in which the right-hand side of the equation is a ...
Example 1 - Finding General Solutions to Differential Equations Using Antidifferentiation Use antidifferentiation to determine the general solution to the differential equation {eq}\dfrac{dy}{dx}=\dfrac{6x}{y+2} {/eq}. Step 1:Rewrite the given differential equation in the form {eq}f...
This paper is concerned with a kind of first-order quasilinear parabolic partial differential equations associated with a class of ordinary differential equations with two-point boundary value problems. We prove that the function given by the solution of
1.1 Definitions And Terminology1.2 Initial-value Problems1.3 Differential Equations As Mathematical ModelsChapter Questions Book Details DIFFERENTIAL EQUATIONS WITH BOUNDARY-VALUE PROBLEMS, 9th Edition strikes a balance between the analytical, qualitative, and quantitative approaches ...
This paper is concerned with global existence of large solutions to the initial-boundary value problem of the planar magnetohydrodynamic compressible flow. Under the assumptions that viscosity and heat conductivity coefficients are constants, magnetic di