Is Y 0 a solution to every differential equation?

This solution obviously works for any linear homogeneous ordinary differential equation, as plugging in y=0 will cause all terms in the equation to go to zero.

Is Y 0 no solution?

If you solve this your answer would be 0=0 this means the problem has an infinite number of solutions. For an answer to have no solution both answers would not equal each other.

What is yy in algebra?

(yy means y multiplied by y, because in Algebra putting two letters next to each other means to multiply them)

What is the answer when 0 0?

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00 is undefined. The expression in and of itself comes into conflict with two facts of arithmetic: any number divided by itself is equal to one , and zero divided by any number is equal to zero .

What if an equation is 0 0?

2 Answers. If you end with 0=0 , then it means that the left-hand side and the right-hand side of the equation are equal to each other regardless of the values of the variables involved; therefore, its solution set is all real numbers for each variable.

What is the solution of the differential equation?

A solution of a differential equation is an expression for the dependent variable in terms of the independent one(s) which satisfies the relation. The general solution includes all possible solutions and typically includes arbitrary constants (in the case of an ODE) or arbitrary functions (in the case of a PDE.)

How do you solve a differential equation with n = 0?

When n = 0 the equation can be solved as a First Order Linear Differential Equation. When n = 1 the equation can be solved using Separation of Variables. For other values of n we can solve it by substituting. u = y 1−n. and turning it into a linear differential equation (and then solve that).

How do you solve differential equations with Wronskian?

And using the Wronskian we can now find the particular solution of the differential equation. d 2 ydx 2 + p dydx + qy = f(x) using the formula: y p (x) = −y 1 (x) ∫ y 2 (x)f(x)W(y 1,y 2) dx + y 2 (x) ∫ y 1 (x)f(x)W(y 1,y 2) dx . Finally we complete solution by adding the general solution and the particular solution together.

When n = 0 the equation can be solved using separation of variables?

When n = 0 the equation can be solved as a First Order Linear Differential Equation. When n = 1 the equation can be solved using Separation of Variables.

Does y = cos ⁡ x satisfy the original equation?

We can try plugging in y = cos ⁡ x and y = sin ⁡ x to the original equation, and we’ll find that they do in fact satisfy. And again, because derivatives don’t care about constant multiples or addition, we can combine these two into one solution