Shyvana's abilities have no cost related to them, and the use of her abilities is only limited by cooldowns. Instead she uses Fury as her secondary resource.
Fury is only needed as a requirement for the use of her ultimate Dragon's Descent, which allows her to change form if she has 100 Fury and remain in that state for as long as she has Fury. Shyvana won't generate Fury unless she has at least one point in Dragon's Descent, and once she puts the first point on the skill she will fill the bar immediately. Any gained Fury will not be lost until her ultimate is used.
Fury of the Dragonborn
Shyvana's melee attacks enhance her abilities.
See the Fury of the Dragonborn entry in each ability's description.
Twin Bite
Cooldown: 10 / 9 / 8 / 7 / 6
Active: Shyvana's next autoattack will strike twice in one swift movement. The second attack will deal physical damage equal to a percentage of her total attack damage. Both attacks will trigger on-hit effects and Fury of the Dragonborn effects.
Dragon form: Twin Bite will damage all units in front of Shyvana when she uses her next autottack instead of just her target. Each unit hit will be dealt on-hit effects and grant fury twice.
Fury of the Dragonborn: Each auto attack reduces the cooldown by 0.5 seconds. This doesn't work on structures.
Second Strike Physical Damage:80 / 85 / 90 / 95 / 100% AD
Burnout
Cooldown: 12
Active: For 3 seconds, Shyvana damages enemies within 162.5 range and has increased movement speed. The bonus movement speed decreases by 15% of its original value per second.
Dragon form: Shyvana now scorches the earth where she walks, leaving a trail of fire for 5 seconds that will continually deal magic damage to enemies that pass over it.
Fury of the Dragonborn: Each auto attack extends the duration of Burnout by 1 second to a maximum of 4 extra seconds. This works on structures.
Active: Shyvana unleashes a fireball forward in a line that affects the first enemy it hits, dealing magic damage to it and reducing its armor by 15% for 4 seconds.
Dragon form: Flame Breath engulfs all units in a cone in front of Shyvana.
Fury of the Dragonborn: Each autoattack that hits debuffed targets will deal 15% of the ability's damage as additional magic damage.
Passive: Shyvana reinforces her scales, increasing her armor and magic resistance. These defensive bonuses are doubled while in dragon form.
Passive Armor & Magic Resistance: 10 / 15 / 20
Active: Shyvana transforms into a dragon and dashes to a target location. Enemies along her path take magic damage and are pushed toward her target location.
Shyvana generates 1 fury every 1.5 seconds while in human form. While in dragon form, she will lose 6 fury every second. Once the fury bar is empty she will return to her normal state.
Fury of the Dragonborn: Each of her autottacks will generate 2 fury. This will allow for Shyvana to prolong the duration of dragon form by attacking. This ability works on structures.
6300 or 
975
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Dragon's Descent, which allows her to change form if she has 100 Fury and remain in that state for as long as she has Fury. Shyvana won't generate Fury unless she has at least one point in 
