how to recognize Bernoulli's equation
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y′+a(x)y=b(x)ym,
where a(x) and b(x) are continuous functions.
If m=0, the equation becomes a linear differential equation. In case of m=1, the equation becomes separable.
In general case, when m≠0,1,Bernoulli equation can be converted to a linear differential equation using the change of variable
z=y1−m.
The new differential equation for the function z(x) has the form:
z′+(1−m)a(x)z=(1−m)b(x)
where a(x) and b(x) are continuous functions.
If m=0, the equation becomes a linear differential equation. In case of m=1, the equation becomes separable.
In general case, when m≠0,1,Bernoulli equation can be converted to a linear differential equation using the change of variable
z=y1−m.
The new differential equation for the function z(x) has the form:
z′+(1−m)a(x)z=(1−m)b(x)
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Answer:
Step-by-step explanation:
y′+a(x)y=b(x)ym,
where a(x) and b(x) are continuous functions.
If m=0, the equation becomes a linear differential equation. In case of m=1, the equation becomes separable.
In general case, when m≠0,1,Bernoulli equation can be converted to a linear differential equation using the change of variable
z=y1−m.
The new differential equation for the function z(x) has the form:
z′+(1−m)a(x)z=(1−m)b(x)
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