Solve for a (complex solution)
a\in \mathrm{C}
f=0\text{ or }c=0
Solve for b (complex solution)
b\in \mathrm{C}
f=0\text{ or }c=0
Solve for a
a\in \mathrm{R}
f=0\text{ or }c=0
Solve for b
b\in \mathrm{R}
f=0\text{ or }c=0
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a\frac{\mathrm{d}(f)}{\mathrm{d}x^{2}}+cf=-b\frac{\mathrm{d}(f)}{\mathrm{d}y^{2}}
Subtract b\frac{\mathrm{d}(f)}{\mathrm{d}y^{2}} from both sides. Anything subtracted from zero gives its negation.
a\frac{\mathrm{d}(f)}{\mathrm{d}x^{2}}=-b\frac{\mathrm{d}(f)}{\mathrm{d}y^{2}}-cf
Subtract cf from both sides.
0=-cf
The equation is in standard form.
a\in
This is false for any a.
b\frac{\mathrm{d}(f)}{\mathrm{d}y^{2}}+cf=-a\frac{\mathrm{d}(f)}{\mathrm{d}x^{2}}
Subtract a\frac{\mathrm{d}(f)}{\mathrm{d}x^{2}} from both sides. Anything subtracted from zero gives its negation.
b\frac{\mathrm{d}(f)}{\mathrm{d}y^{2}}=-a\frac{\mathrm{d}(f)}{\mathrm{d}x^{2}}-cf
Subtract cf from both sides.
0=-cf
The equation is in standard form.
b\in
This is false for any b.
a\frac{\mathrm{d}(f)}{\mathrm{d}x^{2}}+cf=-b\frac{\mathrm{d}(f)}{\mathrm{d}y^{2}}
Subtract b\frac{\mathrm{d}(f)}{\mathrm{d}y^{2}} from both sides. Anything subtracted from zero gives its negation.
a\frac{\mathrm{d}(f)}{\mathrm{d}x^{2}}=-b\frac{\mathrm{d}(f)}{\mathrm{d}y^{2}}-cf
Subtract cf from both sides.
0=-cf
The equation is in standard form.
a\in
This is false for any a.
b\frac{\mathrm{d}(f)}{\mathrm{d}y^{2}}+cf=-a\frac{\mathrm{d}(f)}{\mathrm{d}x^{2}}
Subtract a\frac{\mathrm{d}(f)}{\mathrm{d}x^{2}} from both sides. Anything subtracted from zero gives its negation.
b\frac{\mathrm{d}(f)}{\mathrm{d}y^{2}}=-a\frac{\mathrm{d}(f)}{\mathrm{d}x^{2}}-cf
Subtract cf from both sides.
0=-cf
The equation is in standard form.
b\in
This is false for any b.
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