In the given question as follows , find the general solution of the differential equation using any method: - see the equation as attached heredydx=4−x22x

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In the given question as follows , find the general solution of the differential equation using any method: - see the equation as  attached heredydx=4−x22x

Randall Odom · Accepted Answer

The general solution is a function containing n distinct arbitrary constants, which satisfies a nth order differential equation is said to be a general solution obtained as a sum of the complementary function and a particular integral. The complementary function is the particular integral; it forms the general solution of a linear differential equation. It is essentially an element in the kernel of the differential operator. The differential operator is a symbolic representation of an operation involving differentiation, either ordinary or partial of all parts of the operand, which is a function. The integral equation is an equation that involves the integration of a function. An Integrable is a function that has an integral. To find the general solution of the differential equation cross multiply the dx and integrate both equations using integration by substitution dydx=4−x22x dy=4−x22xdx ∫dy=∫4−x22xdx ∫dy=12∫4−x2xdx u=4−x2 (substitute) u2=4−x2 2u×du=−2xdx (differentiate w.r. to x) 2udu−2x=dx −x2=u2−4 x2=4−u2 x=4−u2 2udu−24−u2=dx −udu4−u2=dx ∫dy=−12∫u4−u24−u2udu y=−12∫u24−u2du Again using integration by substitution substitute u=2v and du=2dv y=−12∫u24−u2du u=2v du=2dv y=−12∫4v2−2dv4−4v2=−12∫4×2v2dv

In the given question as follows , find the general

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